JP2007315759A - Graduation for ratio section - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide measurement graduations for the golden section easily used for drawings and pictures and sufficiently accurate and highly practical even for large parts and small parts. <P>SOLUTION: A plurality of sections having lengths which contract at 0.618, the inverse of the golden ratio, are arranged as an infinite array, and their convergent point is designated as an origin. Small graduation lines are arranged in each section similarly between sections to constitute the graduations for the golden section. Positional relations are detected as the identification number of each section and a reading of the small graduation lines. It is possible to implement a highly practical ratio measuring ruler capable of measuring the golden ratio by three methods in accordance with intended purpose, displaying its size errors, and highly accurately computing a plurality of points of internal division and points of external division in an instantaneous, intuitive, and easily comprehensible manner. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

The present invention is a ratio measurement method and ratio measurement that are easy to find and indicate the proportional relationship of a certain ratio among shapes, patterns, and dimensions, and the division at a certain ratio, that is, the inner and outer dividing points. It relates to ingredients.

For example, bridges in the natural environment, industrial design, editing of photos and printed materials, technical analysis of stock charts, detection of leaks in buried piping, etc. Widely used in many fields. In particular, the golden ratio is emphasized as a ratio that gives a sense of naturalness, comfort, or beauty without any sense of incongruity. In addition to the golden ratio, silver ratio and other ratios may be used.

In order to check or indicate the relationship of these fixed ratios, measure the length and dimensions with a ruler or vernier caliper, etc., calculate the ratio with a calculator, and examine whether it is a fixed ratio. The method is very common. But if you need to examine a large number of dimensions, this is cumbersome and inefficient.

As an example of a measuring tool that directly measures the relationship of the golden ratio, a three-point indicating type divider-like link structure is known. (For example, refer to Patent Document 1) Whether the relationship is the golden ratio or not is indicated by three indication points at the end of the link and can be seen at a glance. However, the angle of opening must be adjusted each time it is measured, and only one point can be specified at a time, and since it is a mechanical instrument, it is expensive and the tip is sharp and dangerous. Therefore, it is not suitable for measuring drawings, design drawings and photographs on a desk.
Japanese Utility Model Publication No. 5-70991

As an example for measuring whether or not the relationship is the golden ratio on a desk, there is a ruler provided with a scale line having a normal length and a scale line obtained by reducing the scale line with the golden ratio. (For example, refer to Patent Document 2) By reading one scale line, the same reading location on the other scale line can be specified as a fixed ratio relationship, that is, the position of the golden ratio. However, at this time, the ruler must be moved and applied to the line to be measured, and there is a problem that only one point having a correspondence relationship can be known.
JP-A-2005-84045

As another example, a method using a golden ratio template using diagonal lines and parallel lines shown in FIG. 16 is generally known. For example, for the line segment A-A, the ratio of the dimensions of a1 and b1, and a2 and b2 is the golden ratio. However, it is difficult to obtain the positional accuracy at the intersection with the oblique line, and it is difficult to see if there are many parallel lines or oblique lines, and conversely, if there are few these lines, it is difficult to visually interpolate and the accuracy is not good. In addition, since the found internal and external dividing points are covered with the template itself, it is impossible to mark the important division points with a writing instrument. In addition, there is a problem in practicality such as the need for the same size as the measurement target.

In discovering and applying the golden ratio, silver ratio, and other fixed ratio relationships that appear in artifacts and natural shapes, you can intuitively determine the fixed ratio relationships and perform mechanical operations. It is an object of the present invention to provide a measuring method and a measuring instrument having good operability, practicality, and accuracy, in which a plurality of dimensional relationships can be investigated at once.

As means for solving the problem, a plurality of sections lined up with reduced length in a certain series at a constant reduction rate, section scale lines separating the sections, and convergence of the geometric series sections The origin scale line arranged on the point and the small scale line which is further subdivided so that the inside of each section can be read with a continuous number, and the small scale arranged in the similar manner at the reduction ratio for each adjacent section. A ratio division scale characterized by comprising a graduation line is used to read the numerical value of the small scale and detect the relationship and position of a certain ratio by corresponding to the same reading position in the other section. This is the main feature.

Here, a certain ratio or a certain reduction ratio means a golden ratio, a silver ratio, or a ratio of other dimensions. However, when the number is 1 or more, the reciprocal number is used in the following description. In other words, the golden ratio is generally 1.618..., The silver ratio is 1.414... In the following explanation, the reciprocal is taken, the golden ratio is 0.618, and the silver ratio is 0. This will be described as 707. More precisely, these numbers are irrational numbers. Of course, 1 as a constant ratio is not included because the convergence point is not located at a finite position in the geometric series and can be measured with a ruler with a normal scale.

According to the ratio dividing scale according to the present invention, one of the given points is aligned with the origin scale line, and the value of the reading of the small scale line of the other point is read, so that it is on a straight line passing through the two points. There is an effect that a plurality of points corresponding to a certain ratio of, for example, two inner dividing points and four outer dividing points of the golden section can be easily read directly.

Therefore, it is easy for anyone to understand how to use, accurate enough to be judged by the human eye, no calculation or machine operation is required, and the position can be directly marked, lightweight and compact However, it does not get in the way, there is no risk of damaging the measurement object, the measurement range is wide, there are no moving parts, there is no failure, no power supply is required, it is inexpensive, easy to handle, wide usage range, easy to handle There are many great benefits of becoming a thing.

In addition, the ratio division scale according to the present invention, the length scale, the ratio division scale of other ratios, and the advantage that the extension part of the ratio division scale of the same ratio can be provided integrally. is there.

The objective of efficiently discovering the dimensional relationships that make up the golden ratio and silver ratio, or applying it from various perspectives, was realized in a low-cost and accurate manner in the same form as a conventional ruler with good operability.

FIG. 1 is a first embodiment of a ruler with a ratio dividing scale according to the present invention. The fixed ratio is set to a golden ratio of 0.618, small scale lines with equal intervals are adopted, and a scale having a length of mm unit is integrally provided in addition to the scale for division according to the present invention.

FIG. 2 shows the structure of the ratio dividing scale according to the present invention with each part disassembled. The most basic part consists of three parts, a section scale line 1, an origin scale line 2, and a small scale line 3. Each section is identified by a section identification symbol 4 such as A, B, C, or the like. A length of 10 cm is assigned to the section A, and small scale lines 3 are attached every 10 mm divided into 10 parts and every 1 mm divided into 100 parts. The section scale line 1 and the small scale line 3 are partially omitted for easy viewing.

In addition, without limitation as in the first embodiment, more generally, the section scale line 1, the origin scale line 2, and the small scale line 3 are not lines as illustrated in FIG. It can be replaced with letters, symbols, figures, numbers, mathematical formulas, colors and patterns. The section identification symbol 4 and the scale number 5 can also be partially or completely omitted, or replaced with other characters, symbols, figures, numbers, mathematical formulas, colors, patterns, or the like.

The length of the section A reduced by the golden ratio 0.618..., 61.8... Mm is assigned to the section B, and a small scale line 3 for 100 equals is attached. . In section C, the interval of the minor scale lines 3 in section B is further reduced by the golden ratio, and a part of the minor scale lines 3 is omitted and 19 minor scale lines 3 are attached. The reading of the scale line can be read as a continuous numerical value from 0 to 99.

That is, even if a part of the minor scale lines 3 is omitted, basically, each section is similar at a constant reduction rate, that is, the interval between the minor scale lines 3 is reduced by the reduction rate, and the corresponding same Consecutive numerical values are arranged, and corresponding points can be read as the same numerical values.

The same applies to the section D and thereafter, but the minor scale line 3 is omitted as the section length decreases. The scale number 5 is given to the small scale line 3 in consideration of easiness of reading, but it is not always necessary.

The method of use will be described with reference to FIG. If the ruler with the ratio dividing scale according to the present invention is used, the object, in this case, the violin, but if the origin scale line 2 is placed at the end thereof, the reading value of the small scale line 3 at the position of the full length a is 51 of the section A is shown, and the minor scale line 3 at the position of b shows the section 51 of the section B and is in the position of the same reading value, so that it is possible to immediately know that a: b is in the golden section relationship. . Further, since the minor scale line 3 at the position of c also indicates 51 of the section C and is the position of the same reading value, it can be immediately known that b: c is also in the golden section relationship. Furthermore, it can be immediately known that the ratios of m and n and u and v are also golden ratios.

The relative relationship of a, b, c, m, n, u, v shown in the figure is established between any sections. That is, by using the ratio division scale according to the present invention, various golden ratio relationships can be easily detected and indicated over the entire length of the ratio division scale. Further, the relationship between a, b, and c in the section closer to the origin scale line 2, for example, the sections G and F and thereafter, makes it difficult to read the scale line, but is separated from the origin scale line 2, for example, sections A and B. If the measurement is shifted to the relationship between m and n in FIG. 4, there is an advantage that detection and instruction can be performed with higher accuracy.

Even if the scale line cannot be read accurately, for example, it is difficult to distinguish between 51 and 52 in the section C, it is because the actual dimension is so small that it cannot be ignored. There is an effect that the accuracy is practically not lowered so much.

When the small graduation lines 3 are made into the small graduation lines 3 at equal intervals as shown in FIG. 3, there is an advantage that a large number of graduations may be moved by the same movement distance in manufacturing, and the position can be easily determined.

When the reduction ratio is the golden ratio, the square of k is 1-k, so the lengths of c and u are equal. That is, the internal dividing points of the line segment a in FIG. The line segment c in FIG. 3 will be described as an example. Inner dividing points are obtained in two places, sections D and E, and outer dividing points are obtained in sections B and A. These internal dividing points are located at the position of the reading value of the same minor tick line 3 next to the right and left of the section of interest and the two adjacent to the same point. And external dividing points can be easily detected and set at once. In addition, since a section where these plural points are present can be seen at a glance, there is an unprecedented great advantage that it is easy to intuitively grasp the approximate positional relationship.

In the ratio division scale according to the present invention, the length is once divided into an infinite array of sections having a geometric series length. If the length of the section A is α and the reduction ratio is k, the length of each section is reduced in a geometric series with a constant reduction ratio in one direction as shown in FIG. They are lined up and separated from each other by section scale lines 1 so that they can be identified. Further, this identification can be assisted by the section identification symbol 4.

Further, the inside of the section is subdivided by small scale lines 3 that can be read with continuous numerical values, and the adjacent small sections are arranged in a similar manner at the reduction ratio, as shown in FIG. The lengths of the readings m on the scale line in each section are arranged in a geometric series with the lengths decreasing. The convergence point of the geometric series section, that is, the position of the origin scale line 2 is obtained by the mathematical formula shown in FIG. 6 and can be arranged at only one fixed position. As shown in FIG. 7, since the distance from the origin scale line 2 is proportional to the reduction ratio, the adjacent section scale lines 1 are obtained by calculating the length from the origin scale line 2 to each section scale line 1. Actually, each section scale line 1 can be drawn and manufactured.

Furthermore, considering the proportional relationship between the lengths of the same reading portions of the small scale line 3 shown in FIG. 5 and the proportional relationship between the lengths of the section scale line 1 and the origin scale line 2 in FIG. Are also in a proportional relationship, and the relationship of FIG. 8 is established. Furthermore, since the difference between the dimensions is also proportional, the relationship of FIG. 9 is also established. That is, across the section scale line 1 and the position where the reading value of the small scale line 3 in each section is the same, each interval is also in a proportional relationship with a certain ratio.

If the scale for division according to the present invention is used, the measurement can be performed by the three methods shown in FIGS. 5, 8, and 9. There is.

For example, the measurement method of FIG. 8 enables a long measurement over the entire length of the ratio dividing scale when the measurement object is long, and the measurement method of FIG. 5 enables a highly accurate measurement when the measurement object is short, The measurement method of FIG. 9 enables the discovery and instruction of a pattern having periodicity of the measurement object.

The above two measuring methods have already been described with reference to FIG. FIG. 10 shows a method for detecting the pattern having the periodicity. The center of FIG. 10 is a dendritic pattern, and a large number of branches are in a golden ratio relationship position. The ruler with the ratio division | segmentation scale concerning this invention is shown in two places. The distance at the center of the dendritic pattern is different from the distance at the tips of many branches. Accordingly, the reading values in each section of the ratio division scale according to the present invention at two locations are all 60 on one side and 13 on the other side when read as 100 scales.

In other words, even if the pattern to be measured has a different interval, if the golden ratio is related, the reading value of each adjacent section can be the same and can be detected, and the reading of the small scale line of each section is the same at each position. If there is no pattern at the position of the origin scale line 2, it is possible to know what kind of golden ratio is related to which part, and the origin scale line 2, that is, the position of the convergence point There is an excellent feature that can be pointed to. Furthermore, even if the position of each branch in FIG. 10 is slightly deviated from the ideal position, it can be easily estimated without any calculation by human judgment. Yes.

As Example 2 of the golden ratio, FIG. 11 shows a case where the small scale lines 3 are scale lines with unequal intervals. The ratio division scale according to the present invention only needs to be similar in proportion to the arrangement of the small scale lines 3 in each section, that is, the positional relationship is proportional to a certain reduction ratio k, as in Example 1 shown in FIG. The same effect can be obtained even if the small scale lines are equally spaced scale lines, or even if they are non-uniformly spaced scale lines as in the second embodiment illustrated in FIG.

FIG. 11 shows that when g is a positive number smaller than 1, the small scale in the section A is located at a position proportional to the power of the k of the dimension S from the origin scale line 2 to the section scale line 1 as the convergence point. A line 3 is arranged from the origin scale line 2 on the convergence point. More specifically, g is arranged every 0.2 from 0.2 to 0.8, and a finer scale line is a small scale line 3 every 0.02 from 0.02 to 0.98. It can be read as a continuous numerical value from 0 to 50. Of course, also in FIG. 11, the equations described with reference to FIGS. 4 to 9 are established, and the three measurement methods are effective.

Further, when a small scale line 3 corresponding to such 50 steps is attached as a scale of power multiplication, there is a feature that an error can be easily estimated. That is, if the difference between the reading of the small scale in the section A and the reading of the section B is e, the dimensional error is naturally 0% if e is 0, but about 1%, 5 if e is 1. In the case of, the error is about 4.7%, in the case of 10, about 9.2%, in the case of 25, the error is 21.4%, and in the case of 50, the error is about 38.2%. In other words, the% value of the error is equal to or less than the difference e of the reading value regardless of the reading value of the small scale in the section A, so that it is possible to immediately know how much dimensional error is present without any calculation. There are other advantages. Note that when the above method is used, the accuracy of error estimation is improved when the small scale line 3 corresponding to 48 steps is attached. Therefore, for example, 95 steps are used to reduce 1/2 of the reading difference e to the error level. Of course, other steps such as an approximate value of% value can be used.

Further, in Example 2 of FIG. 11, an extension portion of the ratio division scale having the same ratio and the section AA are integrally arranged, and if any position on the section A is aligned with the extension straight line, this ruler is used. There is an advantage that the measurement range can be made longer than the length of the ratio division scale by reversing.

FIG. 12 shows an example of the silver ratio with k set to 0.707. A number is used as the section identification symbol 4 and the scale number 5 is omitted. Although the interval of the small scale lines 3 is wider than that of the first embodiment, the intervals between the minimum scale lines are further finely visually interpolated by 1/10, as is generally done with a rod-shaped thermometer. And practically sufficient accuracy can be obtained.

However, unlike the case of the golden ratio, the relationship between the two adjacent sections is not established. Since only one inner point and one outer point can be detected at a time, measurement can be performed by inverting and changing the direction of the origin scale 2. Further, since the relationship between two adjacent sections is a ratio of the square of the silver ratio, for example, an arbitrary small scale line 3 of the section 1 is from the origin scale 2 of the corresponding small scale line 3 of the section 3. There is an effect peculiar to the silver ratio that the midpoint and the double-sized point can be easily specified without performing any calculation because the distance is half the relationship. Although not shown, it is needless to say that the above three measurement methods are possible even with other reduction ratios.

In the third embodiment shown in FIG. 12, the small scale lines 3 in each section are arranged as equally spaced scales of several reduction ratios by the square root of 2, so that by comparing with the dimension values on the drawing, The copying machine has a unique advantage that it is possible to know how the size of a standard sheet such as a drawing has been changed.

In the third embodiment of FIG. 12, the section with the section identification number 0 on the side opposite to the origin scale line 2 is cut in the middle, and the section A is not limited to any length. There is an advantage that it is possible to manufacture without calculating the length α of each time. Furthermore, even division ratio scales having different lengths can be manufactured so that the section lengths are partially the same. Similar to the first embodiment, the three measurement methods are possible.

FIG. 13 shows an example 4 applied to a triangle ruler. Ratio division graduations according to the present invention having the same section length on two sides across a right angle of a right triangle are arranged so that the positions of the origin graduation lines 2 coincide with each other, and sections having a golden ratio relationship are arranged. Since it corresponds with the oblique line, the effect of the first embodiment and the effect that the golden rectangle can be easily detected or the position can be indicated are newly produced.

FIG. 14 also shows the ratio dividing scale according to the present invention in the two directions of the curved scale, and has the same effects as those of the fourth embodiment, and can be easily handled and reduced in weight.

FIG. 15 shows a sixth embodiment in which the ratio division scale according to the present invention is displayed on the computer screen. In order to make use of the golden ratio when designing on a computer screen, creating websites, adjusting computer graphs, adjusting photos, analyzing stock price fluctuation patterns, etc. By displaying the scale for division according to the present invention rather than a display method that shows the result by displaying a dimension line, etc., it appeals to human intuition and makes it easier to find the law in an image or pattern There is an effect. The display on the computer screen can be performed by inputting the information on the position, size and angle of the scale for division according to the present invention stored in advance as a graphic file by inputting or automatically calculating and displaying the deformed graphic. Alternatively, it may be drawn as individual graphic element data, that is, line segments or character information, and the ratio division scale according to the present invention may be configured and displayed.

In addition to the scale division ruler, ruler, triangle ruler, template, underlay, triangle scale, scale plate, tape measure, container, machine, device, instrument scale, etc. It becomes easy to examine the shape and pattern, that is, the ratio of each part such as a real object, a photograph, a picture, a fabric, a drawing, a graph, and an image.

FIG. 1 is a diagram of a division ruler according to the golden ratio of the present invention. Example 1 FIG. 2 is an explanatory diagram of the scale lines in FIG. FIG. 3 is an explanatory diagram of the usage method of FIG. Example 1 FIG. 4 is an explanatory diagram showing the relationship between the lengths of sections. FIG. 5 is an explanatory diagram showing the relationship of the length from each section scale line up to the position of the reading value of the small scale line. FIG. 6 is an explanatory diagram showing mathematical formulas for obtaining the length from the position indicated by the section scale line 1 to the origin scale line 2. FIG. 7 is an explanatory diagram showing the relationship of the length from the position indicated by the section scale line 1 to the origin scale line 2. FIG. 8 is an explanatory diagram showing the relationship of the length from the position indicated by the reading value of the small scale line 3 to the origin scale line 2. FIG. 9 is an explanatory diagram showing the relationship between the positions of the positions indicated by the reading values of the small scale lines 3. FIG. 10 is an explanatory diagram showing a method for measuring a periodic pattern. FIG. 11 shows an example in which the small scale lines 3 are scale lines with unequal intervals. (Example 2) FIG. 12 shows an example of a ruler with scale lines for dividing the silver ratio, wherein k is 0.707. (Example 3) FIG. 13 shows an embodiment applied to a triangle ruler. (Example 4) FIG. 14 shows an example of a curved scale. (Example 5) FIG. 15 is a display example of the scale for division according to the present invention on the computer screen. (Example 6) FIG. 16 shows an example of a conventional golden ratio template using diagonal lines and parallel lines.

Explanation of symbols

1 Section scale line 2 Origin scale line 3 Small scale line 4 Section identification symbol 5 Scale number

Claims (7)

Arranged on the convergence point of the geometric series section, a plurality of sections lined up with a reduction in length in a geometric series with a constant reduction rate in one direction, a section scale line that divides the section The origin graduation line and the small graduation line that is further subdivided so that the inside of each section can be read with a continuous number, and the small graduation line arranged in a similar manner at the reduction ratio for each of the adjacent sections. A scale for ratio division characterized by The ratio division scale of claim 1 is used, and the proportional relationship of the shape and pattern and the ratio division position are read from the value of the small scale line and correspond to the position of the same reading value in the other section. The ratio measuring method characterized by detecting by. 2. The ratio division scale according to claim 1, wherein the small scale lines are arranged so as to divide the section at equal intervals. The scale for division according to claim 1, wherein g is a positive number smaller than 1, and the length from the origin scale line to the section scale line is a power of g times the reduction ratio. The scale for division by division, wherein the small scale line is arranged at a position from the origin scale line. 4. A ruler provided with the ratio dividing scale of claim 3. A ruler provided with the ratio dividing scale according to claim 4. A ratio division scale display program for a computer, comprising the step of displaying the ratio division scale of claim 1 on a screen.

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