CN108039095A - Mathematical probabilities apparatus for demonstrating - Google Patents

Abstract

The invention relates to a mathematical probability demonstration device, which effectively solves the problems of large workload and large human error in the existing needle throwing experimental device; the technical solution is to include a simulated needle bar, a guide device, a needle throwing device, and a needle throwing device Including the fixed shell, the outer side of the fixed shell is connected with fan blades, and the cavity between every two fan blades forms a needle chamber, and the two sides of the four needle chambers are closed and integrally connected with the fixed shell, the first needle chamber There is a first needle-throwing hole vertically facing the direction of the center of the circle, a second needle-throwing hole inclined towards the center of the circle is opened in the second needle-throwing chamber, and a fourth needle-throwing hole is opened in the fourth needle-throwing chamber inclined toward the center of the circle Holes, the first needle-throwing hole, the second needle-throwing hole, and the fourth needle-throwing hole are all connected to each other. The opening of the fourth needle-throwing cavity is provided with a blocking plate. The blocking plate does not close the fourth needle-throwing cavity. The fixed shell The outer wall is connected with the first driving motor through the first rotating shaft; the floor box has strong experimental operability.

Description

Math Probability Demonstration Device

technical field

The invention relates to the technical field of mathematics teaching, in particular to a mathematical probability demonstration device.

Background technique

Probability and statistics are one of the basic contents of mathematics teaching and an important part of modern mathematics. However, when learning probability and statistics, students cannot understand them well because of their abstract nature. At the time of the incident, the teacher could only explain to the students by writing on the blackboard. The students could not understand it thoroughly. During the teaching process, they lacked some auxiliary teaching tools for probability and mathematical statistics. Therefore, the learning efficiency of students was low.

In mathematical probability experiments, there are various common probability experiments, such as the most common coin toss experiment, and another kind of probability experiment device will be introduced in the present invention.

In the 18th century, Buffon raised the following question: Suppose we have a floor paved with parallel and equidistant wood grains. Now randomly throw a needle whose length is smaller than the distance between the wood grains. Find the point where the needle intersects with one of the wood grains. probability. And with this probability, Buffon proposed a method to calculate pi - random needle throwing method, which is Buffon's needle throwing problem.

The basic principles and steps of the experiment are:

1. Take a piece of white paper and draw many parallel lines with a distance of a on it.

2. Take a needle with a length of l (l≤a), randomly throw it n times on the paper with parallel lines drawn on it, and observe the number of intersections between the needle and the line, which is recorded as m.

3. Calculate the probability that the needle intersects the line.

Buffon himself proved that this probability is: p=2l/πa (where π is pi).

Buffon also found that the ratio of the number of favorable throws to unfavorable throws is an expression that includes π. If the length of the needle is equal to a/2, then the favorable throw is changed to 1/π. The more throws are made, the more accurate the value of π can be obtained.

This probability experiment has important mathematical significance. It can not only represent a part of mathematical probability, but also calculate the value of π through probability. Therefore, Buffon’s needle throwing probability experiment is a very important probability experiment in mathematical probability. Students A lot of mathematical probability and calculation of π can be learned from this experiment.

But for the needle-throwing experiment proposed by Buffon, there is no special probability device to demonstrate the probability event. Most of them use the traditional needle-throwing method, that is: draw a line on a white paper, and then throw the needle on the straight line , count the results after throwing the needle one by one.

For this probability demonstration device, there are following deficiencies in the existing situation:

1. There is no special needle throwing probability demonstration device, and the traditional needle throwing experiment is used.

2. In order to better express the probability and calculate the value of π, a large number of counts are required, and the workload caused by manual injection of needles is heavy.

3. There is human error in counting.

4. Artificially throwing the needle, it is inevitable to artificially control the landing position of the needle, thus affecting the probability and π value.

5. Randomness is not reliable.

In view of this, the present invention provides a mathematical probability demonstration device to solve the experimental problem of needle throwing probability proposed by Buffon.

Contents of the invention

In view of the above situation, in order to overcome the defects of the prior art, the present invention provides a mathematical probability demonstration device, which effectively solves the problems of heavy workload and large human error in the existing needle throwing experimental device.

The present invention includes a simulated needle bar, which is a cylindrical rod with uniform length;

A guiding device, the guiding device is a through pipe fixed in the vertical direction, and the simulated needle bar can pass through the through pipe;

A needle-throwing device, the needle-throwing device is fixed below the guide device;

The needle-throwing device includes a circular fixed shell, and four arc-shaped fan blades uniformly distributed on the circumference are integrally connected to the outside of the fixed shell. The clockwise directions of the cavities are called the first needle chamber, the second needle chamber, the third needle chamber, and the fourth needle chamber. Both sides of the four needle chambers are closed and connected with the fixed shell integrally. A first needle injection hole is opened in the first needle injection cavity vertically facing the direction of the center of the circle, a second needle injection hole is opened in the second needle injection cavity inclined to the direction of the center of the circle, and a needle injection hole is opened in the fourth needle injection cavity inclined to the direction of the center of the circle. The fourth needle hole, the first needle hole, the second needle hole, and the fourth needle hole are in an inverted Y shape, and the first needle hole, the second needle hole, and the fourth needle hole are all connected to each other. The opening of the fourth needle chamber is provided with a blocking plate, which does not close the fourth needle chamber, and the outer wall of the fixed shell is connected with the first driving motor via the first rotating shaft;

A floor box, the floor box is placed below the needle-throwing device; the floor box is a box with a cavity inside the upper opening and an arc-shaped bottom wall, and a plurality of horizontally arranged pressure bars are fixed on the upper end of the floor box;

The length of the simulated needle bar is shorter than the distance between the pressing bars.

Preferably, a third needle hole vertically facing the center of the circle is provided in the third needle chamber, and the third needle hole, the first needle hole, the second needle hole, and the fourth needle hole are all connected to each other. connected;

The openings of the first needle-throwing holes are larger than the openings of the second, third and fourth needle-throwing holes;

The first needle-throwing hole and the third needle-throwing hole are vertically connected, and the inner top of the third needle-throwing hole is provided with a radian groove, and a rotatable baffle is arranged in the radian groove, and the baffle can be realized in the radian groove. Swing, the end of the baffle is vertically connected with a rotating plate placed in the fixed shell, the lower end of the rotating plate is rotated and fixed in the fixed shell, a guide hole is opened on the rotating plate, and a guide hole that can move inside is provided in the guide hole. The guide rod is connected to the second rotating shaft through the connecting rod, the second rotating shaft is connected to the second driving motor, and the second driving motor is connected to the first rotating shaft of the first driving motor through the fixed rod, so that the second driving motor follows the first rotating shaft And turn.

Preferably, the fixed shell includes a front fixed shell and a rear fixed shell that are fastened together.

Preferably, one end of the opening of the floor box is fixed with a horizontally arranged horizontal shaft, and a plurality of horizontally uniformly arranged pressure rods are sleeved on the horizontal shaft, one end of the pressure rod is sleeved on the horizontal shaft, and the other end is inserted into the A spring is set on the side wall and the lower end of the floor box, and the lower end of the spring is fixed on the pressing rod. The multiple pressing rods are electronically connected to the same first counter, and the first display screen showing the number of counters is fixed on the outer wall of the floor box. .

Preferably, the upper surface of the pressure rod is coated with paint, the bottom end of the bottom wall of the floor box is equipped with a first vibration motor, the bottom opening of the bottom wall of the floor box is connected with a first conveyor belt, the first The end of the conveyor belt is placed with a rolling plate inclined downward, and the end of the rolling plate is placed with a test plate inclined downward. Rotate upward around the third rotating shaft, the third driving motor is a forward and reverse motor, and a three-dimensional scanner is fixed above the rolling plate, which can detect whether there is pigment on the simulated needle bar, and the three-dimensional scanner controls the start of the third driving motor through a signal. stop, a second conveyor belt is provided under the end of the detection board, a collection box is provided at the end of the second conveyor belt, and the eighth drive motor is connected to the first conveyor belt and the second conveyor belt.

Preferably, the rolling plate is integrally connected with an arc track placed under the detection plate, a contact rod is provided at the end of the arc track, the contact bar is electronically connected with a second counter, and the second counter is connected with a first counter placed on the outer wall of the floor box. Two display screens, the end of the arc track is connected with a cleaning device;

The cleaning device includes an annular cleaning chamber with a cavity inside. The cleaning chamber is placed under the second conveyor belt. The cleaning chamber is provided with a fourth rotating shaft connected to the fourth driving motor. plate, the cleaning plate rotates following the rotation of the fourth shaft, the fourth shaft rotates counterclockwise, the end of the arc track is provided with an inlet on the cleaning chamber, and the other side of the cleaning chamber corresponding to the inlet is provided with an outlet;

A track plate is arranged under the outlet and the second conveyor belt, and a collection box is placed at the end of the track plate.

Preferably, the inside of the upper opening of the collection box is a cavity, the left end of the collection box is arc-shaped, the back side of the collection box is provided with a fixing plate, and the side of the upper right end of the collection box is provided with a support shaft fixed on the fixing plate, collecting The left arc shape of the box runs through the fifth rotating shaft fixed on the fixed plate, so that the collection box can rotate counterclockwise around the fifth rotating shaft. The support shaft can prevent the collection box from turning to the right. On the conveyor belt, the fixed plate drives the collection box to follow the movement of the third conveyor belt. The third conveyor belt is connected to the fifth drive motor, and the fifth drive motor is a forward and reverse motor. The overturning shaft, the top of the overturning shaft and the lower end of the third conveyor belt are fixed with an induction switch, which controls the start and stop and forward and reverse of the fifth drive motor. The inside of the opening is a cavity, and the fourth conveyor belt is installed on one side of the feed box, and the fourth conveyor belt is connected to the sixth drive motor. There is a gap between the fourth conveyor belt and the third conveyor belt, which can ensure that the collection box passes through and the collection box is turned over. Accepts dropped dummy needle sticks in the collection box.

Preferably, the lower end of the feed box is provided with a rectangular first needle outlet, a second vibrating motor is installed on the shell of the feed box, and the lower end of the first needle outlet is communicated with an annular diverter, and the diverter includes a An annular shell connected to the first needle outlet, a rotatable annular body is installed in the annular shell, a plurality of semi-cylindrical grooves uniformly distributed on the circumference are opened on the outer contour of the annular shell, and a sixth driving motor is connected to the annular shell, so that the annular shell The body can rotate in the annular shell, and the lower end of the annular shell communicates with the guide device.

Preferably, the lower end of the annular shell is connected with a steering shell, and a horizontally fixed steering rod is installed in the steering shell. The lower end of the steering shell is a vertical third needle outlet, and the third needle outlet is connected with a needle ring. A rotatable needle-throwing body is installed in the needle ring, and the needle-throwing body is connected with a seventh driving motor. A vertical needle-connecting hole is opened on the outer contour of the needle-throwing body, and the lower end of the needle-throwing body communicates with the guide device.

Preferably, the mathematical probability demonstration device is fixed in a rectangular box.

The invention has ingenious structure, strong experiment randomness, avoids experimental errors caused by human factors, strong experimental operability, accurate experimental results, the whole operation process is convenient for students to observe, and helps students to clearly see the principle of the whole structure , to further increase students' understanding of probability and statistics. In addition to learning probability, they can also understand the calculation of pi.

Description of drawings

Fig. 1 is a schematic perspective view of the perspective view of the present invention.

Fig. 2 is a schematic diagram of a perspective view, a front view, and a sectional view of the present invention.

Fig. 3 is a schematic perspective view of the connection of the feed box, the diverter, and the diverter shell of the present invention.

Fig. 4 is a schematic cross-sectional view of the front view of the connection of the feed box, the diverter, and the diverter shell of the present invention.

Fig. 5 is a schematic diagram of hidden lines inside the perspective view of the needle injection device of the present invention.

Fig. 6 is a schematic cross-sectional view of the needle injection device of the present invention.

Fig. 7 is a schematic perspective view of the floor box of the present invention.

Fig. 8 is a schematic diagram of the connection of the pressing bar, the spring and the pressing bar in the present invention.

Fig. 9 is a schematic perspective view of the rotation driving of the baffle in the present invention.

Fig. 10 is a schematic diagram of the detection plate and cleaning device of the present invention.

Fig. 11 is a schematic diagram of the collection box fixing device of the present invention.

Detailed ways

The aforementioned and other technical contents, features and effects of the present invention will be clearly presented in the following detailed description of the embodiments with reference to the accompanying drawings 1 to 11 . The structural contents mentioned in the following embodiments are all based on the accompanying drawings of the description.

Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.

The present invention is a mathematical probability demonstration device, which mainly demonstrates the needle-throwing experimental device proposed by Buffon. The experimental device can not only realize the statistics of probability, but also realize the calculation of π value through the probability experimental device. The present invention mainly Describe and draw out its structural schematic diagram, for described fixing etc. connection methods, all adopt the commonly used connection methods such as common bolt fixing, welding fixing, also have, because parts and components are many, possible in the accompanying drawing of the present invention Some dimensions may be drawn inaccurately, but this does not affect the structural principle and implementation of the present invention.

Embodiment 1, a kind of mathematical probability demonstrative device, includes analog awesome stick 1, is used for completing the needle throwing experiment of the present invention, in order not to affect the error caused by the structure of the simulated needle stick 1 itself to the experiment, the simulated needle stick 1 is designed as The cylindrical rod body has a uniform length, and the material can be metal, stainless steel, or hard plastic.

Guide device 2, guide device 2 is a through-pipe placed vertically, and through-pipe is fixed on the rectangular box body 68, and its structure is exactly common cylinder, and there is through-hole in the middle of it, and its diameter size can be simulated needle Stick 1, so that the simulated needle stick 1 falls in a vertical state.

Needle-throwing device 3, the needle-throwing device 3 is fixed below the guide device 2, the needle-throwing device 3 is not connected to the guide device 2, the needle-throwing device 3 includes a circular fixed shell 4, and the outer wall of the fixed shell 4 passes through the first rotating shaft 14 is connected with a first drive motor to make the fixed shell 4 rotate. The first drive motor can be connected to a reducer to control the speed of the fixed shell 4. The outer ring surface of the fixed shell 4 is integrally connected with four arc-shaped fan blades 5. The fan blade 5 does not play the role of blowing air, but is only used as a divided cavity. There are four fan blades 5, which are evenly distributed around the circumference and divided into four cavities. For a better description, we start with The top is called the first needle chamber 6, and the clockwise direction is called the second needle chamber 7, the third needle chamber 8, and the fourth needle chamber 9. The two sides of the four needle chambers are also closed. The shells are integrally connected with the outer wall of the fixed shell 4 and the outer wall of the fan blade 5 respectively. A first needle-throwing hole 10 is opened in the first needle-throwing chamber 6. The direction of the first needle-throwing hole 10 faces the center of the fixed shell 4. The first needle-throwing hole 10 The opening of the needle-throwing hole 10 is relatively large, occupying the entire first needle-throwing chamber 6 , and it becomes smaller first when it goes down, and then remains unchanged to ensure that the simulated needle bar 1 dropped in the first needle-throwing chamber 6 falls off. When it falls into the first needle-throwing chamber 6, it must enter the first needle-throwing hole 10, and the second needle-throwing chamber 7 is provided with a second needle-throwing hole 11 inclined toward the center of the circle, and the fourth needle-throwing chamber 9 is provided with an inclined The fourth needle-throwing hole 12 toward the center of the circle, the opening size of the second needle-throwing hole 11 and the fourth needle-throwing hole 12 can not be so large, so that the simulated needle bar 1 is in the second needle-throwing chamber 7 or the fourth needle-throwing chamber When 9 falls, it can enter the second needle-throwing hole 11 or the fourth needle-throwing hole 12, or directly in the second needle-throwing chamber 7 or the fourth needle-throwing chamber 9 without entering the second needle-throwing chamber. In the hole 11 or the fourth needle hole 12, the first needle hole 10, the second needle hole 11, and the fourth needle hole 12 are connected to each other, and the shape is an inverted Y shape. The opening of the four needle chambers 9 is provided with a blocking plate 13, the blocking plate 13 is equivalent to a closing plate, but the blocking plate 13 does not close the fourth needle chamber 9. To make the analog needle bar 1 enter and exit the gap, the fixed housing 4 is rotating, and the rotation relies on the first driving motor connected through the first rotating shaft 14 .

After the simulated needle bar 1 falls from the needle-throwing device 3, it enters the landing box 15. The landing box 15 is directly below the needle-throwing device 3. The inside of the upper opening of the landing box 15 is a cavity, and its bottom wall is preferably curved. It is beneficial for the simulated needle bar 1 to roll down on the bottom wall of the floor box 15, and the upper end of the floor box 15 is fixed with a plurality of pressing bars 16, and there are multiple pressing bars 16 arranged horizontally, but they themselves are vertically arranged, when the simulated needle bar 1 After falling, touching the upper surface of the pressure bar 16 means that it intersects with a straight line, and those that do not touch the upper surface of the pressure bar 16 directly fall into the floor box 15, and according to the experimental requirements of Buffon, the simulated needle bar 1 The length is shorter than or equal to the distance between every two pressing bars 16, and in order to avoid the simulated needle bar 1 from being stuck between the pressing bars 16, the present invention makes the length of the simulated needle bar 1 shorter than the distance between the pressing bars 16. distance, which has no other effect on the experiment.

In the specific experimental operation, the simulated needle bars 1 are put into the guide device 2 one by one, and the simulated needle bars 1 fall vertically into the needle-throwing device 3, and the fixed shell 4 is always rotating. In order to express better, we Assuming that the fixed shell 4 rotates in the counterclockwise direction, the simulated needle bar 1 has a probability of falling into the first needle chamber 6, the second needle chamber 7, the third needle chamber 8, and the fourth needle chamber 9, thereby increasing the Simulates the randomness of the drop of needle stick 1.

Assuming that the simulated needle bar 1 falls into the first needle-throwing chamber 6, the opening of the first needle-throwing hole 10 is relatively large, so the simulated needle-bar 1 must enter the first needle-throwing hole 10, and then randomly from the second needle-throwing hole 10 No matter where the needle falls from the pinhole 11 or the fourth needle-throwing hole 12, the randomness of the simulated needle bar 1 can be increased.

Assuming that the simulated needle bar 1 falls into the second needle-throwing chamber 7, then the simulated needle-bar 1 may enter the second needle-throwing hole 11, or may fall into the second needle-throwing chamber 7 without entering the second needle-throwing chamber. hole 12, then the simulated needle bar 1 will slide down due to gravity when it rotates to the bottom following the fixed shell 4, and it may also enter from the second needle-throwing hole 12, randomly from the fourth needle-throwing hole 12 or the first needle-throwing hole 10 Falling further increases the randomness of the simulated needle bar 1.

Assuming that the simulated needle bar 1 falls into the cavity of the third needle 8, the simulated needle bar 1 rotates following the fixed shell 4, and when the third needle cavity 8 rotates downward, the simulated needle bar 1 falls.

Assuming that the simulated needle bar 1 falls into the fourth needle-throwing chamber 9, then the simulated needle-bar 1 may enter the fourth needle-throwing hole 12, may fall into the fourth needle-throwing chamber 9, and not enter the fourth needle-throwing chamber hole 12, then the simulated needle bar 1 slides down due to gravity when it rotates to the bottom following the fixed shell 4, and it is also possible to enter from the second needle hole 11, randomly from the second needle hole 11 or the first needle hole 10 Falling further increases the randomness of the simulated needle bar 1.

In fact, except that the way the simulated needle bar 1 falls is random, the present invention randomizes the falling position of the simulated needle bar 1 , thereby further increasing the randomness of the simulated needle bar 1 .

The simulated needle bar 1 falls from directly above, but not necessarily from directly below. In addition to falling directly below, the simulated needle bar 1 can also fall from the left or right directly below. The simulated needle bar 1 is explained above. The position when it fell, the following describes the position of the falling point after the fall, specifically:

When the simulated needle bar 1 fell into the first needle-throwing chamber 6, if the simulated needle-bar 1 fell out from the fourth needle-throwing hole 12, then due to the reason of the blocking plate 13, the simulated needle bar 1 would finally fall from the right side directly below. Falling out, if the simulated needle bar 1 falls out from the second needle throwing hole 11, the simulated needle bar 1 falls out from the left side directly below.

When the simulated needle bar 1 fell into the second needle-throwing cavity 7, if the simulated needle-bar 1 did not enter the second needle-throwing hole 11, the simulated needle bar 1 would fall out from the left side directly below, when the simulated needle bar 1 enters the second needle-throwing hole 11 and falls out from the fourth needle-throwing hole 12, then the simulated needle bar 1 falls from the right side directly below, when the simulated needle bar 1 enters the second needle-throwing hole 11 and falls out from the first needle-throwing hole When the needle-throwing hole 10 falls out, the simulated needle bar 1 may fall out from directly below or on the left side directly below.

When the simulated needle bar 1 fell into the third needle-throwing cavity 8, the simulated needle bar 1 fell out from the left side directly below.

When the analog needle bar 1 fell into the fourth needle chamber 9, the analog needle bar 1 could not enter due to the blocking of the blocking plate 13, and the blocking plate 13 was not a completely closed plate. After the blocking plate 13 turned over, the analog Needle bar 1 will inevitably enter the fourth needle-throwing cavity 9, if the simulated needle bar 1 does not enter the second needle-throwing hole 11, then the simulated needle bar 1 will fall out from the right side directly below, if the simulated needle bar 1 enters the second needle-throwing hole 11 When the four needle-throwing holes 12 fall out from the first needle-throwing hole 10, the simulated needle bar 1 falls out from the right side directly below. 11 When falling out, the simulated needle bar 1 falls out from directly below or on the right below.

The needle throwing device of the present invention can greatly increase the randomness of the simulated needle bar 1, and will not be affected by the outside world, thereby ensuring the accuracy of the data experiment, and the randomness will not affect the experiment except for ensuring the accuracy of the experimental data. error.

No matter where the simulated needle bar 1 falls from and where it falls, the simulated needle bar 1 all falls into the floor case 15, because the length of the simulated needle bar 1 is shorter than the distance between the pressing bars 16, the simulated After the needle bar 1 falls, there are only two cases of touching and not touching the upper surface of the pressing bar 16. When the simulated needle bar 1 falls, if it touches the upper surface of the pressing bar 16, it means that it intersects the straight line. If it touches the upper surface of the pressure rod 16, it means that it does not intersect with the straight line. No matter whether it intersects with the straight line or not, the simulated needle bar 1 will fall to the bottom of the floor box 15, and it can be collected at last to complete all the intersecting and non-intersecting with the straight lines. count. Then the probability of intersecting and non-intersecting can be calculated, and the pi can be calculated according to the formula.

Embodiment 2, on the basis of Embodiment 1, in order to further enhance the diversity of dropping of the needle throwing device 3 and increase the randomness of falling, we also have a third throwing needle in the third throwing needle chamber 8. Pinhole 17, the third needle-throwing hole 17 is the same as the first needle-throwing hole 10 and is all vertically towards the center of circle direction, the third needle-throwing hole 17 is the same as the first needle-throwing hole 10, the second needle-throwing hole 11, the fourth throwing-pin hole The pinholes 12 are all connected, and the first needle-throwing hole 10 and the third needle-throwing hole 17 are equivalent to being vertically connected. The only difference is that the opening size of the third needle-throwing hole 17 is smaller than the opening of the first needle-throwing hole 10. The opening sizes of the second needle-throwing hole 11, the third needle-throwing hole 17, and the fourth needle-throwing hole 12 are the same. In the cavity 8, it is also possible to drop into the third needle-throwing hole 17, and its purpose is all in order to increase the randomness when the simulated needle bar 1 falls.

If the third needle-throwing hole 17 communicates with the first needle-throwing hole 10, the simulated needle bar 1 dropped from the first needle-throwing hole 10 will directly fall out of the third needle-throwing hole 17, and there is a high probability that it will not fall from the first needle-throwing hole 10 again. The second needle-throwing hole 11 and the fourth needle-throwing hole 12 fall out. Of course, this situation does not affect the experimental nature of the simulated needle bar 1. However, the present invention will increase the randomness when it falls, and finally make the simulated needle No matter which one of the four needle-throwing chambers the rod 1 falls from, there will be different falling-out and different landing positions, so that the four needle-throwing chambers all have their own characteristics.

The top of the third needle-throwing hole 17, that is, the center of the circle, is provided with a radian groove 18. The radian groove 18 takes the third needle-throwing hole 17 as the middle position, and both sides are provided with a radian groove. There is a rotatable baffle 19 inside, and the baffle 19 can rotate in the arc groove 18, so as to realize the opening and closing of the baffle 19 to the third needle-throwing hole 17, and the opening and closing is to prevent the needle from the first needle-throwing hole 10. The dropped analog needle bar 1 uniquely falls out from the third needle-throwing hole 17. When the analog needle bar 1 fell into the first needle-throwing hole 10, if the baffle plate 19 was opened, the analog needle bar 1 would fall from the third needle-throwing hole 17. The needle hole 17 falls out, and the simulated needle bar 1 falls out from directly below. If the baffle plate 19 is closed, the simulated needle bar 1 falls out from the second needle-throwing hole 11 or the fourth needle-throwing hole 12.

And the rotatable structure of baffle plate 19 is: the structure in the 3rd throwing pin hole 17 has only baffle plate 19, and the device of driving baffle plate 19 is all fixed in fixed shell 4 inside, therefore can not affect the analog needle bar 1 Drop, the lower end of the rotating plate 20 is fixed in the fixed shell 4 by rotation, as the rotating fulcrum of the rotating plate 20, a guide hole 21 is provided on the rotating plate 20, and a guide rod 22 is arranged in the guide hole 21, and the guide rod 22 is in the Movement in the guide hole 21, the guide hole 21 is used as a movement track, the guide rod 22 is connected to the second rotating shaft 24 through the connecting rod 23, and the second rotating shaft 24 is connected to the second driving motor 25, thereby driving the guide rod 22 to move in the guide hole 21 , to realize the swing of the baffle plate 19, and the second drive motor 25 is connected to the first drive motor through the fixed rod 26, because the baffle plate 19 will follow the rotation of the fixed shell 4 in addition to rotating in the arc groove 18 itself, therefore, it is necessary to Follow the rotation of the first driving motor.

Embodiment 3, on the basis of Embodiment 1, in order to facilitate the production of structures such as installing the baffle plate 19 and manufacturing the radian groove 18, the fixed shell 4 is divided into a front fixed shell and a rear fixed shell, so that the driving structures such as the baffle plate 19 Put them in it, and then fasten them together, and finally they all rotate following the rotation of the first driving motor.

Embodiment 4, on the basis of Embodiment 1, in addition to manual counting, automatic counting can also be realized. Specifically, one end of the opening of the floor box 15 is fixed with a horizontally arranged horizontal shaft 26. The horizontal shaft 26 does not rotate. A plurality of pressing rods 16 are sheathed on the shaft 26. The spacing between the pressing rods 16 is the same. And can rotate around transverse axis 26, the other end of depression bar 16 is inserted on the other side wall of floor box 15, and this position has a slotted hole on the side wall of floor box 15, and depression bar 16 is inserted in the slot hole, The pressure rod 16 can rotate up and down at this end, and a spring 27 is sleeved below the pressure rod 16 at this position. When the pressure rod 16 is compressed downward, it will be reset by the spring 27. There is a pressing rod 28 under the spring 27. There are multiple pressing rods 16, and there are multiple corresponding pressing rods 28, but multiple pressing rods 28 are connected to the same first counter, and the counting display of the first counter will be displayed on the first display screen 29. 29 is fixed on the shell of floor case 15, can all see each count clearly. There are many kinds of counters, including mechanical counters, electronic counters, etc., or the principle of some electronic watches is also a counter, and counters will not be described here as a prior art.

After the simulated needle bar 1 falls from the needle-throwing device 3, it will enter the landing box 15. At this time, there are two states, one is to press the pressure bar 16, and the other is not to press the pressure bar 16. When the simulated needle bar 1 touches the pressure When the upper surface of the rod 16 is on the upper surface, the pressing rod 16 will be pressed downwards, and the pressing rod 16 will contact the pressing rod 28 through the spring 27, and the pressing rod 28 will display the count on the first display screen 29, and if the analog needle bar 1 has not Pressing the push bar 16 will not count on the first display screen 29 .

Embodiment five, on the basis of embodiment one, except above-mentioned counting, the present invention can also adopt another kind of counting device, is coated with colored pigment 30 on the pressure bar 16 upper surface, and this pigment 30 and analog pin bar 1 has different colors and is easy to clean. For example, paints such as water powder, ink, and watercolor can be selected. A first vibrating motor 31 is installed at the bottom of the bottom wall of the floor box 15 to speed up the falling of the dropped analog needle bar 1. In order to prevent the simulated needle bar 1 from falling to the bottom wall of the floor box 15 and staying without rolling, an opening is provided at the end of the bottom wall of the floor box 15, and a first conveyor belt 32 is placed and fixed at this position, and the first conveyor belt 32 is connected with Drive the driving motor that the first conveyor belt 32 rotates, the end of the first conveyor belt 32 is obliquely placed with a rolling plate 33 downwards, and the end of the rolling plate 33 is also placed and fixed with an obliquely downward detection plate 34, the right end of the detection plate 34 passes through a The fixed and rotatable third rotating shaft 35 is connected, and the third rotating shaft 35 is driven by the third driving motor. If the third rotating shaft 35 rotates clockwise first, the detection plate 34 is rotated upwards, and then reversed to the original position after rotating a certain angle. Therefore, the third driving motor is preferably a forward and reverse motor, and a three-dimensional scanner 36 is fixed above the rolling plate 33 to scan and detect whether there is paint 30 on the analog needle bar 1, and the three-dimensional scanner 36 is a 3D scanner is a scientific instrument used to detect and analyze the shape (geometric structure) and appearance data (such as color, surface albedo, etc.) of objects or environments in the real world. 3D scanner36 As a prior art, it will not be described in detail here. The start-stop and forward and reverse of the third driving motor are controlled by the electric signal sent by the three-dimensional scanner 36, and the second conveyor belt 37 is also placed at the end of the detection plate 34. The end of the second conveyor belt 37 is provided with a collection box 38 for collecting the simulated needle bar 1. The first conveyor belt 32 and the second conveyor belt 37 are respectively connected with driving motors, which we call the eighth driving motor.

During specific use, if the simulated needle bar 1 touches the paint 30 on the pressure rod 16, the simulated needle bar 1 will be stained with paint, no matter whether it touches the paint 30, the simulated needle bar 1 will eventually fall into the floor case 15 , no matter what state the simulated needle bar 1 falls into the bottom wall of the floor box 15, the vibration of the first vibration motor 31 will make the simulated needle bar 1 roll down from the arc-shaped bottom wall, and then enter the first conveyor belt 32 , move to the rolling plate 33 through the first conveyor belt 32, and the simulated needle bar 1 rolls down freely on the rolling plate 33, so the three-dimensional scanner 36 must be able to scan the paint 30 on the simulated needle bar 1, if the three-dimensional scanner 36 scans To the paint 30, a signal will be sent to the third drive motor, so that the detection plate 34 rotates clockwise, or rotates upwards. At this time, the analog needle bar 1 on the rolling plate 33 will not roll down to the detection plate 34 on, but fall from the bottom of the detection plate 34, if the three-dimensional scanner 36 does not scan the paint 30, then the three-dimensional scanner 36 will not send a signal to the third drive motor, and the detection plate 34 will not rotate, simulating the needle bar 1 Continue to roll from the rolling plate 33 onto the detection plate 34 , then move from the detection plate 34 to the second conveyor belt 37 , and finally fall into the collection box 15 .

Embodiment 6, on the basis of Embodiment 5, an arc track 39 placed below the detection plate 34 is integrally connected below the rolling plate 33, and a contact rod 40 is installed on the bottom wall of the end of the arc track 39, and the contact rod 40 electronically A second counter is connected to count the simulated needle sticks 1 stuck with paint. The second counter is connected to a second display screen 41. A cleaning device 42 is connected to the end of the arc track 39 to count the simulated needle sticks 1. The paint 30 on is cleaned.

And the cleaning device comprises the annular cleaning bin 43 that the inside is a cavity, and the cleaning bin 43 is placed below the second conveyer belt 37, and the cleaning bin 43 is connected with the fourth driving motor, and the fourth driving motor is connected with the fourth rotating shaft 44, and the fourth driving motor drives the fourth driving motor. The four rotating shafts 44 rotate, and the annular cleaning chamber 43 does not follow the rotation when rotating. The fourth rotating shaft 44 is connected with a plurality of cleaning plates 45 uniformly distributed on the circumference. The cleaning plates 45 follow the rotation of the fourth rotating shaft 44 and rotate. The cleaning plates 45 The length is from the center of the circle to the inner wall of the cleaning chamber 43. The annular cleaning chamber 43 is provided with an inlet 46. The inlet 46 is at the end of the arc track 39, so that the simulated needle bar 1 can roll down into the cleaning chamber 43. Except for the inlet 46, the cleaning Storehouse 43 is provided with exit 47, and exit 47 is symmetrical center with the center of circle, is arranged on the other side of cleaning storehouse 43, is all provided with track plate 48 below exit 47 and second conveyor belt 37, and the end of track plate 48 is placed with The collection box 38 is used to collect the simulated needle bar 1, and there are multiple cleaning plates 45 in the cleaning interior 43, which rotate in the cleaning chamber counterclockwise.

During specific use, the simulated needle bar 1 that has detected the pigment falls from the bottom of the detection plate 34 onto the arc track 39, touches the contact rod 40, and then counts on the second counter, thereby being used to count the number of pigments , the simulated needle bar 1 falls into the cleaning chamber 43 from the arc track 39, and the fourth rotating shaft 44 in the cleaning chamber 43 drives the cleaning plate 45 to clean the simulated needle bar 1. Water and detergent are placed in the cleaning chamber 43 to facilitate the cleaning of the paint Cleaning is carried out, and the simulated needle bar 1 after cleaning falls out from the cleaning chamber 43, and then falls into the collection box 38. A device for catching the water spilled in the cleaning chamber 43 can be provided below the cleaning chamber 43. If there is If necessary, water leakage holes can be provided on the required parts of the structure.

Embodiment seven, on the basis of embodiment six, the inside of the opening of the upper end of the collection box 38 is a cavity, the left end of the collection box 38 is arc-shaped, the back side of the collection box 38 is provided with a fixing plate 49, and the upper end of the right side of the collection box 38 Be fixed with supporting shaft 50, and supporting shaft 50 is fixed on the fixed plate 49, is mainly used in preventing collection box 38 from overturning to the right, makes collection box 38 be the rightmost end of turning right when making collection box 38 in vertical state, the left side of collection box 38 The side wall is arc-shaped, and the left side wall runs through the fifth rotating shaft 51 fixed on the fixed plate 49. The collecting box 38 is free to rotate and can rotate around the fifth rotating shaft 51. The collecting box 38 can only rotate around the fifth rotating shaft 51 from the beginning. Rotate counterclockwise, can only turn to the left, and fixed plate 49 is fixed on the 3rd conveyer belt 52 that is inclined to place, and 3rd conveyer belt 52 is driven by the 5th driving motor 53, and the 5th driving motor 53 is the forward and reverse motor, One side of the left end of the collection box 38 is fixed with an overturning shaft 54 placed above the third conveyor belt 52, the overturning shaft 54 is fixed, and the two ends of the third conveyor belt 52 are respectively provided with an induction switch 55, which controls the fifth drive. The start and stop of motor 53 and forward and reverse, one side above the third conveyer belt 52 is also fixed with feed box 56, and the inside of the upper end opening of feed box 56 is cavity, and the side of feed box 56 is equipped with the 4th conveyer belt 57, The fourth conveyor belt 57 is driven by the sixth drive motor, and there is a gap between the fourth conveyor belt 57 and the third conveyor belt 52 without contact, because the gap will allow the collection box 38 to pass through.

During specific use, it falls into the collection box 38 to simulate the needle bar 1 moving upwards following the movement of the third conveyor belt 52. When the collection box 38 touches the overturning shaft 54, the collection box 38 rotates around the fifth rotating shaft 51, simulating The needle bar 1 turns inside out from the collection box 38 and falls onto the fourth conveyor belt 57, and then moves into the feed box 56 through the fourth conveyor belt 57. The initial state of the collection box 38 is a vertical vertical state, because the support shaft 50 Reason, can not turn to the right, overturns collection box 38 through overturning shaft 54, then collection box 38 freely resets to original position, and induction switch 55 is used for controlling the positive and negative rotation and start-stop of the 3rd conveyor belt 52.

In the present invention, after the collection box 38 collects a certain amount or after all the simulated needle sticks 1 have been tested, they can be started again, and multiple batches of experiments can be carried out, so that the total number of simulated needle sticks 1 can be better determined, or multiple times can be obtained. A large number of experiments can improve the accuracy of the experimental probability.

Embodiment eight, on the basis of embodiment seven, the lower end of the feed box 56 is provided with a rectangular first needle outlet 58, the purpose is to drop out one by one, and the shell of the feed box 56 The second vibrating motor 59 is installed on it, and the purpose is to be used for ordering the simulated needle bar 1 that falls randomly in the feeding box 56, so that the stuck simulated needle bar 1 can drop out from the first needle outlet 58 smoothly.

In order to prevent multiple analog needle bars 1 from falling out at once, an annular diverter 60 is communicated with the lower end of the first needle outlet 58. The diverter 60 includes an annular shell 61, and the annular shell 61 communicates with the first needle outlet 58. A rotatable annular body 62 is installed in the shell 61, and the sixth driving motor is connected to the annular body 62, so that the sixth driving motor drives the annular body 62 to rotate in the annular shell 61, and a plurality of half cylinders are arranged on the annular body 62. Groove 63, the analog needle bar 1 falls in the semi-cylindrical groove 63, and then falls out when following the rotation to just below.

Embodiment 9, on the basis of Embodiment 8, the lower end of the annular shell 61 is connected with a steering shell 63, and a steering rod 64 is fixed horizontally in the steering shell 63, because the simulated needle bar 1 falls down laterally, and the needle throwing device below 3 The opening is small, so it is necessary to change the falling direction of the simulated needle bar 1 to become a vertical drop. Therefore, the simulated needle bar 1 falls from the annular shell 61 into the steering shell 63 and changes direction through the steering rod 64, while the steering shell 63 is similar to a conical shape, with a large opening at the upper end and a small opening at the lower end. The lower end of the steering shell 63 is the third vertical needle outlet. The falling speed is too fast, and when the needle-throwing device 3 is not completed, another simulated needle stick 1 will also fall down, and the two simulated needle sticks 1 may collide or get stuck, so we need to place the next The falling speed of one simulated needle bar 1 slows down, so the third needle outlet is connected to the needle-throwing ring 65, and the needle-throwing body 66 is installed in the needle-throwing ring 65, and the needle-throwing body 66 is rotated by the seventh driving motor, and the needle-throwing body There is only one vertical needle connection hole 67 on the 66, which is used to connect the simulated needle bar 1, and the next simulated needle bar 1 needs to wait for the needle body 66 to rotate for one week before it can be connected, and the needle body 66 can also be connected A speed reducer is used to ensure the speed at which the simulated needle bar 1 falls. Finally, the simulated needle bar 1 falls into the through pipe of the guide device 2 from the needle connection hole 67 in a vertical state.

A plurality of driving motors and vibrating motors in the present invention are all small motors, and can be fixed.

In the tenth embodiment, on the basis of the first embodiment, the parts of the above-mentioned mathematical probability demonstration device are fixed in the rectangular box 68 .

In the present invention, when the simulated needle sticks fall one by one, they are collected into the collection box. After all the simulated needle sticks are collected, the second experiment and multiple experiments are carried out, or the collection box is started after a certain number is reached, and the material is fed. At the beginning, multiple simulated needle sticks were loaded into the box at one time, and then dropped out one by one for experiments.

The invention has ingenious structure, strong experiment randomness, avoids experimental errors caused by human factors, strong experimental operability, accurate experimental results, the whole operation process is convenient for students to observe, and helps students to clearly see the principle of the whole structure , to further increase students' understanding of probability and statistics. In addition to learning probability, they can also understand the calculation of pi.

Claims (10)

1. The mathematical probability demonstration device is characterized in that, comprising: A simulated needle bar (1), the simulated needle bar (1) is a cylindrical rod with uniform length; A guide device (2), the guide device is a through pipe fixed in the vertical direction, and the simulated needle bar (1) can pass through the through pipe; A needle-throwing device (3), the needle-throwing device (3) is fixed below the guide device (2); The needle throwing device (3) includes a circular fixed shell (4), and four arc-shaped fan blades (5) uniformly distributed around the circumference are integrally connected to the outer side of the fixed shell (4), and each two fan blades (5 ) forms the needle cavity, and the four needle cavities are called the first needle cavity (6), the second needle cavity (7), the third needle cavity (8), and the clockwise direction respectively. The fourth needle chamber (9), the two sides of the four needle chambers are closed and integrally connected with the fixed shell (4), and the first needle chamber (6) is provided with a first needle vertically facing the center of the circle hole (10), the second needle injection chamber (7) is provided with a second needle injection hole (11) obliquely facing the direction of the center of the circle, and the fourth needle injection chamber (9) is provided with a fourth needle injection chamber (9) which is obliquely facing the direction of the center of the circle Holes (12), the first needle-throwing hole (10), the second needle-throwing hole (11), the fourth needle-throwing hole (12) are inverted Y-shaped, the first needle-throwing hole (10), the second needle-throwing hole (11), the fourth needle-throwing holes (12) are all connected to each other, the opening of the fourth needle-throwing chamber (9) is provided with a blocking plate (13), and the blocking plate (13) does not block the fourth needle-throwing chamber (12) ) is closed, and the outer wall of the fixed shell (4) is connected with the first driving motor via the first rotating shaft (14); A floor box (15), the floor box is placed under the needle-throwing device (3); the floor box (15) is a box with a cavity at the top opening and an arc-shaped bottom wall, and the floor box (15) The upper end is fixed with a plurality of horizontally arranged pressing rods (16); The length of the simulated needle bar (1) is shorter than the distance between the pressing rods (16). 2. The mathematical probability demonstration device according to claim 1, characterized in that, a third needle-throwing hole (17) vertically facing the center of the circle is opened in the third needle-throwing chamber (8), and the third needle-throwing hole is The hole (17), the first needle-throwing hole (10), the second needle-throwing hole (11), and the fourth needle-throwing hole (12) are all connected to each other; The openings of the first needle-throwing hole (10) are larger than the openings of the second needle-throwing hole (11), the third needle-throwing hole (17) and the fourth needle-throwing hole (12); The first needle-throwing hole (10) and the third needle-throwing hole (17) are vertically connected, and the inner top of the third needle-throwing hole (17) is provided with a radian groove (18), and the radian groove (18) is provided with There is a rotatable baffle (19), the baffle (19) can swing in the radian groove (18), and the end of the baffle (19) is vertically connected with a rotating plate (20) placed in the fixed shell (4). ), the lower end of the rotating plate (20) is rotated and fixed in the fixed shell (4), the rotating plate (20) is provided with a guide hole (21), and the guide hole (21) is provided with a guide rod ( 22), the guide rod (22) is connected to the second rotating shaft (24) through the connecting rod (23), the second rotating shaft (24) is connected with the second driving motor (25), and the second driving motor (25) is connected to the second rotating shaft (26) through the fixed rod (26). ) is connected to the first rotating shaft (14) of the first driving motor, so that the second driving motor (25) rotates following the first rotating shaft (14). 3. The mathematical probability demonstration device according to claim 1, characterized in that, the fixed case (4) comprises a front fixed case and a rear fixed case which are fastened together. 4. The mathematical probability demonstration device according to claim 1, characterized in that, one end of the opening of the floor box (15) is fixed with a horizontally arranged horizontal shaft (26), and the horizontal shaft (26) is sleeved with multiple A horizontally uniformly arranged pressure rod (16), one end of the pressure rod (16) is sleeved on the horizontal axis (26), the other end is inserted on the side wall of the floor box (15) and the lower end is sleeved with a spring (27 ), the lower end of the spring (27) is fixed on the pressing rod (28), and the plurality of pressing rods (28) are electronically connected to the same first counter, and the first display showing the number of counters is fixed on the outer wall of the floor box (15) screen (29). 5. The mathematical probability demonstration device according to claim 1, characterized in that, the upper surface of the pressure rod (16) is coated with paint (30), and the bottom end of the bottom wall of the floor box (15) is installed with The first vibrating motor (31), the bottom opening of the bottom wall of the landing box (15) is connected with a first conveyor belt (32), and the end of the first conveyor belt (32) is placed obliquely downward with a rolling plate (33), The end of the rolling plate (33) is placed with an inclined downward detection plate (34), the right end of the detection plate (34) is connected through the third rotating shaft (35), and the third rotating shaft (35) is connected with the third drive motor, so that the detection The left end of the plate (34) can rotate upwards around the third rotating shaft (35), the third driving motor is a forward and reverse motor, and a three-dimensional scanner (36) is fixed above the rolling plate (33), which can detect the analog needle bar ( 1) Whether there is pigment (30) on the surface, the three-dimensional scanner (36) controls the start and stop of the third drive motor through the signal, and the second conveyor belt (37) is installed under the end of the detection plate (34), and the second conveyor belt (37) A collection box (38) is provided at the end, and the eighth driving motor is connected to the first conveyor belt (32) and the second conveyor belt (37). 6. The mathematical probability demonstration device according to claim 5, characterized in that, the rolling plate (33) is integrally connected with an arc track (39) placed under the detection plate (34), and the end of the arc track (39) A contact rod (40) is provided, and the contact rod (40) is electronically connected to a second counter, which is connected to a second display screen (41) placed on the outer wall of the floor box (15), and the end of the arc track (39) is connected to There is a cleaning device (42); The cleaning device includes an annular cleaning chamber (43) with a cavity inside, the cleaning chamber (43) is placed under the second conveyor belt (37), and the fourth rotating shaft (44) connected to the fourth driving motor is arranged in the cleaning chamber (43). ), the fourth rotating shaft (44) is connected with a plurality of cleaning plates (45) uniformly distributed on the circumference, the cleaning plate (45) rotates following the rotation of the fourth rotating shaft (44), and the fourth rotating shaft (44) rotates counterclockwise, An inlet (46) on the cleaning chamber (43) is opened at the end of the arc track (39), and an outlet (47) is opened on the other side of the cleaning chamber (43) corresponding to the inlet (46); A track plate (48) is arranged under the outlet (47) and the second conveyor belt (37), and a collection box (38) is placed at the end of the track plate (48). 7. The mathematical probability demonstration device according to claim 6, characterized in that, the inside of the upper opening of the collection box (38) is a cavity, the left end of the collection box (38) is arc-shaped, and the back of the collection box (38) is The side is provided with a fixed plate (49), the side of the upper right end of the collection box (49) is provided with a support shaft (50) fixed on the fixed plate (49), and the left arc shape of the collection box (38) runs through a The fifth rotating shaft (51) on the plate (49) makes the collection box (38) rotate counterclockwise around the fifth rotating shaft (51), and the support shaft (50) can prevent the collection box (38) from turning over to the right, and fix the plate (49) is fixed on the third conveyor belt (52) placed obliquely, so that the fixed plate (49) drives the collection box (38) to follow the movement of the third conveyor belt (52), and the third conveyor belt (52) is connected with the fifth drive motor ( 53), the fifth drive motor (53) is a forward and reverse motor, and the left end side of the collection box (38) is fixed with a tipping shaft (54) placed on the top of the third conveyor belt (52), and the tipping shaft (54) An induction switch (55) is fixed on the top and the lower end of the third conveyor belt (52). Feed box (56), the inside of the upper opening of the feed box (56) is a cavity, and a fourth conveyor belt (57) is installed on one side of the feed box (56), and the fourth conveyor belt (57) is connected to the sixth drive motor, There is a gap between the fourth conveyor belt (57) and the third conveyor belt (52), which can ensure that the collection box (38) passes through and can receive the simulated needle sticks ( 1). 8. The mathematical probability demonstration device according to claim 7, characterized in that, the lower end of the feed box (56) is provided with a rectangular first needle outlet (58), and the shell of the feed box (56) A second vibrating motor (59) is installed, and the lower end of the first needle outlet (58) is communicated with an annular diverter (60). The diverter (60) includes an annular shell (61) communicated with the first needle outlet (58). ), the annular shell (61) is equipped with a rotatable annular body (62), and the outer contour of the annular shell (61) is provided with a plurality of semi-cylindrical grooves (63) uniformly distributed around the circumference, and the annular shell (61) is connected with The sixth driving motor enables the annular body (62) to rotate in the annular shell (61), and the lower end of the annular shell (61) communicates with the guide device (2). 9. The mathematical probability demonstration device according to claim 8, characterized in that, the lower end of the annular shell (61) is connected with a steering shell (63), and a horizontally fixed steering rod (64) is installed in the steering shell (63) , the lower end of the steering shell (63) is the third vertical needle outlet, the third needle outlet is connected with the needle ring (65), and the rotatable needle body (66) is installed in the needle ring (65) , the needle body (66) is connected with the seventh drive motor, a vertical needle hole (67) is provided on the outer contour of the needle body (66), and the lower end of the needle body (66) communicates with the guide device (2 ). 10. The mathematical probability demonstration device according to claim 1, characterized in that the mathematical probability demonstration device is fixed in a rectangular box (68).