GB2317119A - Educational system of shapes - Google Patents

Abstract

An array of shapes comprises first shapes which are shaped to be right-angled isosceles triangles ("unit triangles"), second shapes which are squares made up of two unit triangles, third shapes which are lozenges made up from two unit triangles, fourth shapes which are triangles made up from two unit triangles and fifth shapes which are triangles made up from four unit triangles. A set of 24 such shapes are each coloured with a respective colour derived from a specified colour wheel. Extra shapes can be provided to make exact rectangular forms.

Description

Educational Svstem of ShaPes Field of the Invention This invention relates to a didactic puzzle-assembly in the form of an integral set of shapes comprising a plurality of suitably shaped elements in visually distinguishable classes. where the classes are specified by the element sizes and shapes, which are mathematically related, and by the elements being coloured according to a defined set of colours.

Background of the Invention Conventionallv, there have been available various sets of blocks and shaped pieces, mainly directed for use by young children, where the blocks or elements are selfcoloured, stained or painted with a limited selection of colours. The pieces are intended to be arranged to make patterns or designs.

In relation to this, a Chinese game called Tangram' is popularly known which comprises a square which is split into seven geometric forms. From these basic forms, various planar forms can be imitated or crealed which utilise all of the available elements.

This prior game structure has the disadvantage of only comprising seven elements and, even when coloured. the colouring is not related to a didactic colour system or to the various available shapes or sizes.

There are other comparable game structures based on the principle of sub-dividing two < limensional geometric forms which generally have a larger number of elements. Again the shapes and sizes are not so designed as to be able to provide an extensive variety of tessellated patterns within a mainly rectangular or square frame; nor can they be used to demonstrate mathematical relationships. At the same time. any colouring of the elements is determined bf mere decoration rather than being related to the teaching of the science of colour and colour mixing.

Thus currently. there are not available systems of shaped blocks with a particular attribute of area size related to square roots of length, that may be arranged into planar decorative and tessellated patterns. The attribute of area would be that the blocks have an integrated mathematical progression of area size, related to square roots of the length of a block side. This size progression would be such that the user, through manipulation of the pieces, may grow to understand and appreciate the phenomena of square numbers, square roots and proportionality of length or area.

Further. there is no system of shaped blocks with particular functional attributes of colour and of colour arrangement, such that the blocks may be used for more than mere use as coloured blocks for play or design. The attribute of colour would be that colours are specified and allocated to the various shaped blocks according to a planned progression of colours around a defined colour wheel. The attribute of colour arrangement would comprise the various sizes and shapes of the blocks being coloured in accord with various groups within this colour wheel. Thus. in conjunction with explanatory lexts, the shapes would be able to be used to illustrate a scientific. perception-based system of defining, describing, naming and specifying different colours.

Objects of the Invention It is now a primary object of this invention to provide a novel didactic assembly which provides an integrated system for both learning and understanding mathematical and other scientific and artistic topics and for use as a work-tool or a tessellating puzzle or toy.

Another object of the assembly, in conjunction with suitable accompanying texts written by the inventor or others under his supenision, is to provide physical demonstration of the various colours in a specified colour wheel and their relationships to one another.

A further object of the assembly is the ability to provide wider manipulation of the tessellations and the arrangements of the shapes and their colours by making available a suitable computer graphics programme and documentation.

These objects are accomplished essentially by a didactic assembly defined by a block subdivided into suitable elements each element being coloured with one colour from a set of specified colours comprising a defined colour wheel of specified spectral and non-spectral colours.

Summary of the Invention Thus, in this invention a didactic puzzle-assembly is proposed which is defined by an integral set of shapes comprising a plurality of shaped and coloured elements. The forms of these elements is based on a fundamental unit shape, comprising a right-angled isosceles triangle with two sides of specified unitlength and the third side of 42 unit-length. Each of the elements either is in the form of this fundamental triangular polygon (or 'unit-triangle') or is one of further and larger elements mathematically related by being configured into multiples of the fundamental triangular polygon just described. These further and larger elements comprise two unit squares, two-unit lozenges, two-wlit triangles or four-unit triangles. All of the elements are characterized by concurrently each being coloured differently according to specified colours from a defined colour wheel made up of three defined primary colours. three defined secondary colours, six defined tertiary colours and twelve defined quaternary colours.

The sizes of the elements may be further inter-related to specified colours or to specified groups of colours.

The elements of triangular, rectilinear or lozengal form may be placed side by side to form a tessellated assembly or the elements may be sorted according to the various shapes and colours of which the comprise.

The elements or blocks are provided in a basic set of twenty-four shapes, an arrangement that comprises forty-eight unit-triangles. In addition to this basic set, there are other combinations of the block shapes available to extend or vary the basic set.

This basic set also may be equipped with a tray or frame of suitable dimensions in which the elements or blocks may be arranged in various orientations to form tessellated assemblies or patterns or designs.

Brief description of the Drawings The invention may be more clearly understood, together with further features and advantages, from the following description of some embodiments of the didactic assembly according to the invention anda in particular, of a preferred embodiment thereof. illustrated by the accompanying drawings, where: Figure 1 shows the various component elements in a perspective view: Figure 2 shows in perspective a preferred embodiment of this didactic assembly as a whole together with a basic unit-triangle element which illustrates how the shape of a complete square may be formed from various embodiments. the numbering of the shapes concordant with the numbering of the elements in Figure 1, Figure 3 is a plan view of the preferred embodiment showing, by means of numbering the shapes, the distribution of each of the specified colours for this embodiment: Figures 4 and 5 show a second preferred embodiment, the numbering of the shapes concordant with the numbering of the elements in Figure 1 and the references to colours are as for Figure 3; Figures 6 to 13 show some examples of the two-dimensional configurations that may be achieved with this didactic assembly (the numbering of the shapes concordant with the numbering of the elements in Figure 1), where Figures 6 and 7 show two further arrangements of the first preferred embodiment in which the elements are arranged in a '5 byS' grid (as the elements are arranged in Figures 2 and 3); Figures 8,9 and 10 show arrangements of the first preferred embodiment in which the elements are arranged as a freeçformat assembly of the elements that incorporates use of both 'S by 5' and '7 by 7' shape orientations. the cooss-hatched shading indicating areas within the square framework which are unoccupied by any element: Figures 11, 12 and 13 show arrangements of the elements of first preferred embodiment in which the elements are arranged in a '7 by 7' grid. which requires all elements to be turned 450 from the orientation provided for in a '5 by 5' grid (illustrated in Figures 2, 3, 6 and 7).

Description of tbe preferred embodiment A specific embodiment of the invention will now be described by way of example only, with reference to accompanying diagrammatic drawings in which various modifications to size and material may be made without departing from this invention.

Making references to the drawing views, and in particular Figures 1 to 3, a didactic assembly according to the invention essentially comprises a plurality of elements (Figure 1) defining a planar block (Figure 2) in which, concurrently, the twenty-four colours of a defined colour wheel may be assigned one to each of the 24 shaped elements (Figure 3). The colours to which the numbers in Figure 3 refer are: colour 1 "Red" (primary) colour 13 "Cyan" (secondary) colour 2 "Coral" (quaternary) colour 14 "Sky" (quaternary) colour 3 "Orange" (tertiary) colour 15 "Cobalt Blue" (tertiary) colour 4 "Tangerine" (quaternary) colour 16 "Indigo" (quaternary) colour 5 "Yellow" (secondary) colour 17 "Blue-violet" (primary) colour 6 "Peridot" (quaternary) colour 18 "Plum" (quaternary) colour 7 "Lime" (tertiary) colour 19 "Purple" (tertiary) colour 8 "Apple" (quaternary) colour 20 "Mallow" (quaternary) colour 9 "Green (primary) colour 21 "Magenta" (secondary) colour 10 "Leaf" (quaternary) colour 22 "Rhodium" (quaternary) colour 11 "Aquamarine" (tertiary) colour 23 "Raspberry" (tertiary) colour 12 "Turquoise" (quaternary) colour 24 "Mulberry" (quaternary) colour 25 neutral colour - "lead-gro, " or "field-grey." The above colours are defined more closely in a later section - 'Technical description and commentarv on the colour attributes of the invention'.

The planar solid block (no.6 in Figure 2) in this preferred embodiment is generally configured as an irregular hexagonal prism with two opposing sides 6a at right angles to two opposing sides 6b, the pairs of sides 6a and 6b oppose each other and abut a third pair of opposing sides 6c. The length of the sides 6a and 6b are each 4 unit-lengths and the length of sides 6c is 2 unit-length. The said irregular hexagonal prismatic block 6 may be of any desired height 6e, up to a ma::iiuum height of three-tenths of a unit-length, suitable to the chosen material and to the aesthetic considerations concerning the use of essentially planar tiles or elements into which the block 6 is sub-divided.

In the preferred embodiment shown in the drawings, Figures 1 to 3, the block 6 of planar hexagonal shape is subdivided into twenty-four elements including first prismatic bodies 1, second prismatic bodies 2, third prismatic bodies 3, right quadrangular prisms or right parallelepipedons 4 and irregular quadrangular prisms or irregular parallelepipedons 5.

With reference to the drawings in Figure 1: The first prismatic bodies 1 are in the form of eight right prisms. These right prisms 1 each have a base lbofarea la. This base lb is defined by an isosceles right triangle the cathetus whereof. indicated at Ic. is defined as being of one 'unit-length' and the third side or hypotenuse, indicated at ld, is defined as being of 42 unit-length. The hypotenuse Id coincides with sides 6c in the assembled block illustrated in Figure 1. The first prismatic bodies 1 are designated as 'unit-triangles'; the second prismatic bodies 2 are in the form of four right prisms. These right prisms each have a base 2b of area 2a. This base 2b is defined by an isosceles right triangle the cathetus whereof, indicated at 2c. is defined as being equal in length to the hypotenuse Id of the base of the first prismatic body, that is of 2 unit-length; the third side or hypotenuse of these second prismatic bodies, indicated at 2d. is defined as being equal in length to twice the length ofthe cathetus ic of the first prismatic body 1, that is of two unit-lengths. The area 2a of the base 2b of the second prismatic body 2 is twice the area la of the first prismatic body 1; the third prismatic bodies 3 are in the form of four right prisms. These right prisms 3 each have a base 3b of area 3a. This base 3b is defined by an isosceles right triangle the cathetus whereof, indicated at 3c, is defined as being equal in length to the hypotenuse 2d of the base of the second prismatic body 2. that is of two unit-lengths; the third side or hypotenuse of these third prismatic bodies, indicated at 3d, is defined as being equal in length to twice the length of the cathetus 2c of the second prismatic body 2, that is of 2 2 unit-lengths. The area 3a of the base of the third prismatic body 3 is twice the area 2a of the second prismatic body 2 and four times the area la of the first prismatic body 1; the fourth bodies 4 are in the form of four right quadrangular prisms or right parallelepipedons, each having a base 4b of area 4a. This base 4b is defined by the sides 4c arranged at right angles to each other these sides 4c being ofthe same length as the cathetus ic of the first prismatic body 1. that is one unit-length. Thus these prismatic bodies 4 have the plan of a square. The area 4a of the square base 4b is twice that of the first prismatic body 1; the fifth bodies 5 are in the form of irregular quadrangular prisms or irregular parallelepipodons 5, four in number, each having a base 5b of area 5a. This base Sb of each irregular quadrangular prism is defined by two opposing sides Sc of the aforesaid unit length and the two other sides 5d being equal in length to the hypotenuse id of the first prismatic bodies 1 (that is 42 unit-lengths). The sides are so arranged that two opposing internal angles Sf are of 450 each and the other two opposing angles 5g are of 1350 each. The area 5a of the base 5b of each irregular quadrangular prism or parallelepipedon 5 is twice that of the first prismatic body 1; for all these shapes previously described that is the prismatic bodies 1, 2 and 3, the right and irregular parallelepipedons 4 and 5, the height of the body (le, 2e, 3e, 4e or 5e respectively) is determined to be at maximum three tenths (3110 or 0-3) of the unit-length. The minimum height may be chosen at the manufacturer's discretion determined by ease of handling and by the strength of the manufacturing material used.

Additional novelty of this embodiment is shown in Figure 3. This drawing illustrates each element coloured with one of twenty-four specified colours. These specified colours are the three defined primary colours. the three defined second colours, the six defined tertiary colours and the twelve defined quaternary colours listed above, the definitions for the colours being specified in the later section 'Technical description and commentary on the colour attributes of the invention'.

The first' second and third prismatic bodies may be referred to loosely as 'small'. 'medium' and 'large' 'triangles' respectively. The right quadrangular prisms may be referred to loosely as 'squares.

The irregular quadrangular prisms may referred to loosely as 'lozenges'.

In a first preferred embodiment of this invention, there is provided a set of twenty-four elements.

each based on a specified unit triangle. The set comprises four four-unit 'triangles', four two-unil 'triangles', four two-unit 'squares'. four two-unit 'lozenges' and eight one-unit 'triangles', in all forty-eight units.

All the above shapes may be made from suitable natural or man-made materials that allow for accurate colouration according to the colour details given for Figure 3 which are specified in a later section - 'Technical description and commentary on the colour attributes of the invention'.

A second preferred embodiment is shown in Figures 4 and 5. This embodiment of the didactic assembly utilises fourteen elements. Thirty-two unit-triangles are employed in its disposition, this disposition being shorn in Figure 6 and the numbering of shapes is accorded with the numbering of Figure 1. Additional novelty of this embodiment is shown in Figure 5. This Figure illustrates that each element is coloured with one of twelve specified colours (two colours each being used on two elements).

The specified colours are the three defined primary colours, the three defined secondary colours and the six defined tertiary colours.

The patent is not compromised by the use of colours different from those specified herein. Nor is this patent compromised by using uncoloured shapes.

Technical description and commentary on the mathematical attributes of the invention This system of shaped elements, in the preferred embodiment, allocates 48 unit-triangles with two sides of one unit-length and a hypotenuse of 42 unit-length to 24 elements. each coloured with one of 24 specified colours. It will be noted that 48 is a number very close to 49, which has an exact square-root of seven (449 = 7).

It should be noted that 48 unit-triangles can also be regarded as 96 half-unit-triangles. It will be noted that 96 is a number very close to 100, which has an exact square-root often (4100 = 10).

Further, the 48 units may be regarded as 24 double-unit-triangles or 'square-units'. It will be noted that 24 is a number very close to 25 that has an exact square-root of five (425 = 5).

The twenty-four elements of the first preferred embodiment may be placed within assemblies termed as a '5 by 5' grid (Figures 2 and 3, 8, 9) or a '7 by 7' grid (Figures 13, 14, 15).

The unitary length in a '5 by 5' grid is of length one unit. Thus the area of a '5 by 5' grid is (5 x 5) square-units or 25 square-units. Each square-unit has the area of two unit-triangles. so a S by 5' grid contains 50 unit-triangles.

The unitary length in a '7 by 7' grid is of length half the hypotenuse of a unit-triangle. that is (1/242) unit-length. This length, (l/242) units, is the same as a length of 0.7071 units. Thus, the length of the side of a '7 by 7' grid is (7 x 0.7071) units or 4.9497 units. Therefore. the area of a .7 by7' grid is 24.50 square-units. Each square-unit has twice the area of a unit-triangle, so a '7 by 7' grid contains (24.5 x 2) unit-triangles or 49 unit-triangles.

These two types of assembly are distinguished by the orientation in which the elements of the assembly are placed. By turning all individual elements by 450, the user shifts from using a '5 by 5' grid to using a '7by7'grid,orfromusinga '7 by 7' grid to using a 'SbyS' grid.

For a more free-format assembly of the pieces that incorporates use of both shape orientations.

(Figures 8. 9, 10), a further frame, base or tray may be provided. The length of the sides of this frame is determined by the sum of the length of a side (2 units) plus the length of the hypotenuse (2i2 units), both the side and the hypotenuse being of a four-unit triangle: thus free-format assembly frame side-length = (2+2 12) unit-lengths. This length, (2+2z12) units, is the same as a length of 4.8284 units. Therefore. the area of such a base would be 23.314 square-units. Each square-unit has trice the area of a unit-triangle. so a free-format assembly grid contains (23.314 x 2) unit-triangles or 46.63 unittriangles.

Different sized bases (7 by 7' grid. '5 by 5' grid, free-format grid with an area of 46.63 unittriangles) may be used to enhance the aesthetic arrangements available. Examples of these arrangements may be made available in various forms such as a book or booklet accompanying the set of shapes or a screen representation obtained by using a computer programme developed by the inventor.

It will be noted that all three types of assemblies discussed above are very close to one another in area: that is they contain 46-63 unit-triangles, 49 unit-triangles or 50 unit-triangles, all of which cluster closely around 48 unit-triangles. The reader will recall that 48 is the number of unit-triangles found in the first preferred embodiment of 24 elements. Therefore, it would be possible to place the same set of elements. that is the twenty-four elements of the first and preferred embodiment, into all three different types of assembly within a single square-shaped frame, base, grid or tray, if minor adjustments are made.

This frame would be of dimensions 5 unit-lengths by 5 unit-lengths. Each square-unit has twice the area of a unit-triangle. so the frame would contain (25 x 2) or 50 unit-triangles.

With a '5 by 5' assembly, two extra unit-triangles would be required to complete the shape of a square. With a '7 by 7' assembly, two extra half-unit-triangles would be required to complete the shape of a square. These extra triangles may be provided with a preferred embodiment or as individual additional blocks. With the free-form assembly of the shapes, however. which has an area of 46.6 unittriangles, the completion of a regular square cannot be attained Aesthetic arrangements of spacing 'fillets' or other shapes would be used to complete the form of a square (shaded areas in Figures 8. 9.

10).

Thus. a set of the first preferred embodiment may be sold with a frame or tray which has the dimensions of 5 unit-lengths bs 5 unit-lengths. The size of this tray or frame is chosen to accommodate pieces being placed in any orientation. Additional pieces, two extra unit-triangles and two extra halfunit-triangles, may be provided with this frame or tray.

Other less closely integrated sets may be provided for decorative purposes, for colour work for use with younger children or to allow larger sets to be built up from a series of smaller sets.

Technical description and commentary on the colour attributes of tbe invention Whereas systems for describing and specifying colours which are available currently attempt to provide a means to classify any colour that may be encountered in the natural world or generated by chemical svnthesis, the colouring of this invention is intended to provide a structure of specified colours incremented through a complete wheel of visible colours, both spectral and non-spectral.

There are available manse systems for defining, describing and specifying colours. Some colour systems have their origins in the biological and physical phenomena of colour and in scientific definitions. Other systems of colour are based on the craft trade of house decoration. the biases of fashion and culture and the limitations of the perception of the human eye.

The specified colours described in this invention provide a complete colour wheel of both spectral and non-spectral colours within the visible wavelengths. This specified colour wheel ranges from red.

through orange to yellow, through green to can blue, through purple and violet to magenta and so back to red. Other elements may be coloured from a range of subsidiary colours which are still under development.

In this invention there are twenty-four colours of a defined colour wheel which may be used to colour any object or be used to help teach colour perception theory or the discussion of colour names.

The defined colour wheel is made up of primary. secondary, tertiary and quaternary colours.

The three primary colours are those colours to which the three perceptual cones of the eye respond red. green and blue-violet. The three secondary colours - yellow, magenta and cyan - are intermediary to the primary colours. The six tertiary colours are intermediate to the primary and to the secondary colours. The twelve quaternary colours are intermediate to the primary, secondary and tertiary colours.

The secondary colours are those obtained bst mixing the responses of two of the perpeptl cones of the eye, while the tertiary and quaternary colours are intermediate hues based on perception and wavelength.

Loose definitions of these twenty-four colours are listed at the end of this section, where the Natural Colour System (NCS) of Sweden references, the wave-length values, the Pantone * Color numbers and the Commission Internationale de l'Eclairage (CIE) x(A) and y(A) values are merely approximate and the final colour achieved will be dependant on and determined by any limitations imposed by manufacturing processes. All values given are prcnisional, are still in the process of determination and may not be precise. More precise colour definitions will be dependant on further research and refinement.

*PANTONE 19 is a registered trademark of Pantone. Inc

Colour NCS Wavelength *PANTONE CIE (Sweden) in rim Color x(X) 1 Red 1080 R 620 P199 0.5372 0.3074 2 Coral 0090 Y80R 603 P595 0.5824 0.3448 3 Orange 0090 YSOR 590 P151 0.5432 0.4018 4 Tangerine Y23R 582 P137 0.4911 0.4383 S Yellow 0080 Y 575 P109 0.4524 0.481 6 Peridot 0080 G70Y 569 P386 0.4189 0.5103 7 Lime 0080 G40Y 562 P374 0.3703 0.5204 8 Apple 0080 G20Y 549 P368 0.2992 0.5106 9 Green 2070 G 508 P3415 0.2322 0.4236 10 Leaf 2060 B70G 494 P3285 0.2072 0.3304 11 Aquamarine 2060 B50G 489 P320 0.202 0.3025 12 Turquoise B25G 485 P3125 0.1945 0.2642 13 Cyan 1070 B 481 P299 0.1813 0.2223 14 Ska 1060 R90B 477 P2925 0.1787 0.1698 15 Cobalt blue R83B 470 P293 0.1834 0.1388 16 Indigo R65B 450 P2725 0.2308 0.1624 17 Blue-violet 4050 R50B 430 P259 0.2500 0.1800 18 Plum R45B -544 P254 0.3223 0.2017 19 Purple R40B -530 P246 0.3407 0.2216 20 Mallow R35B -518 P240 0.3605 0.2347 21 Magenta R30B -507 Pantone Rhodamine Red 0.3795 0.2304 22 Rhodium R25B 498 P226 0.4149 0.2576 23 Raspbem R20B 496 P214 0.4392 0.2674 24 Mulberry 1080 R1OB -493 P137 0.5211 0.2831 25 Lead-grey 6010 R70B Field-grey 7010 GlOY In lieu of colours described in this Patent. you may use the PANTONE t Colors above, the standards for which are shown in the curenl edition of the PANTONE Color Guide 1000.

*PANTONE s is a registered tra

Claims (30)

Claims

1 A didactic puzzle-assembly defined by an integral set comprising a plurality of shaped and coloured elements, the forms of the elements being based on a fundamental unit shape; comprising a right-angled isosceles triangle with two sides of specified unit-length and the third side of 42 unitlength, where each of these elements either is such a fore-mentioned fundamental triangular polygon (or 'unit-triangle'), or is one of further and larger elements mathematically related by being configured into multiples of the fundamental triangular polygon just described, these further and larger elements comprising two-unit triangles, four-unit triangles, two-unit squares and two-unit lozenges; all of these elements are characterized by concurrently each being coloured differently according to specified colours from a defined colour wheel made up of three defined primary colours, three defined secondary colours, six defined tertiary colours and twelve defined quaternary colours.

2 A didactic assembly according to Claim 1, wherein the proportions of its elements are based on the smallest planar dimension being defined as of one unit-length, whatever length in uficture is chosen as this smallest planar dimension, and all other planar dimensions being multiple proportions of this unit-length.

3 A didactic assembly according to Claims 1 and 2, wherein it comprises a plurality of small or one-unit triangles with the dimensions of the base being one unit-length, those of the cathetus being one unit-length and those of the hypotenuse being 2 unit-length, and of medium or two-unit triangles with the dimensions of the base being 2 unit-length, those of the cathetus being n12 unit-length and those of the hypotenuse being 2 unit-lengths, and of large or four-unit triangles with the dimensions of the base being two unit-lengths, those of the cathetus being two unit-lengths and those of the hypotenuse being 242 unit-lengths, and of two-unit squares with the dimensions of each side being one unit-length, and of two-unit lozenges with the dimensions of each side being one unit-length, the sides so arranged that two opposing internal angles are of 45" each and the other two opposing angles are of 135" each.

4 A didactic assembly according to Claim 3, wherein it comprises eight small or one-unit triangles, four medium or two-unit triangles, four large or four-unit triangles.

four two-unit, four two-unit lozenges; an arrangement of twenty-four elements composed offortyeight fundamental unit-triangles.

5 A didactic asseniv according to Claims 1 to 4, wherein that each element be coloured in one of twenty-four specified colours, the specified colours providing a complete colour wheel of both spectral and non.spectral colours within the visible wavelengths. This specified colour wheel ranges from red, through orange to yellow, through green to cyan blue, through purple and violet to magenta and so back to red. Other dements may be coloured with neutral colours "lead-grey" or "field-grey" or from a range of subsidiary colours which are still under develapment These shaped elements are coloured with one of the colours specified as follows:

Colour NCS Wavelength PANTONE#* CIE (Sweden) in nm Color x(#) y(#) 1 Red 1080 R 620 P199 0.5372 0.3074 2 Coral 0090 Y80R 603 P595 0.5824 0.3448 3 Orange 0090 Y50R 590 P151 0.3432 0.4018 4 Tangaine Y23R 582 P137 0.4911 0.4383 5 Yellow 0080 Y 575 Pl09 0.4524 0.481 *PANTONE is the registered trade mark of Pantone, Inc

Colour NCS Wavelength PANTONE E9* CIE (Sweden) in nm Color x(X) y(X) 6 Peridot 0080 G70Y 569 P386 0.4189 0.5103 7 Lime 0080 G40Y 562 P374 0.3703 0.5204 8 Apple 0080 G20Y 549 P368 0.2992 0.5106 9 Green 2070 G 508 P3415 0.2322 0.4236 10 Leaf 2060 B70G 494 P3285 0.2072 0.3304 11 Aquamarine 2060 B50G 489 P320 0.202 0.3025 12 Turquoise B25G 485 P3125 0.1945 0.2642 13 Cyan 1070 B 481 P299 0.1813 0.2223 14 Sky 1060 R9OB 477 P2925 0. 1787 0.1698 15 Cobaltblue Mue R83B 470 P293 0.1834 0.1388 16 Indigo R65B 450 P2725 0.2308 0.1624 17 Blue-violet 4050 RSOB 430 P259 0.2500 0.1800 18 Plum R45B -544 P254 0.3223 0.2017 19 Purple R40B -530 P246 0.3407 0.2216 20 Mallow R35B -518 P240 0.3605 0.2347 21 Magenta R30B -507 Pantone Riiodimine Red 0.3795 0.2304 22 Rhodium R2SB -498 P226 0.4149 0.2576 23 Raspherry R20B -496 P214 0.4392 0.2674 24 Miberry 1080 R1OB -493 P137 0.5211 0.2831 25 Lead-grey 6010 R70B Field-grey 7010 G1OY In lieu of colours described in this Patent. you may use the PANTONE 9 Colors above, the standards for which are shown in the current edition of the PANTONE Color Formula Guide 1000.

PANTONE is the registered trade mark of Pantone, Inc.

6 A didactic assembly according to Claim 1,2 and 3. wherein it comprises four small or one-unit triangles with the dimensions of the base being one unit-length, those of the cathetus being one unit-length and those of the hypotenuse being 2 unit-length, two medium or two-unit triangles with the dimensions of the base being q2 unit-length, those of the cathetus being 2 unit-length and those of the hypotenuse being 2 unit-lengths, four large or four-unit triangles with the dimensions of the base being two unit-lengths, those of the cathetus being two unit-lengths and those of the hypotenuse being 2x2 unit-lengths, two two-unit squares with the dimensions of each side being one unit-length, twounit lozenges with the dimensions of each side being one unit-length, the sides so arranged that two opposing internal angles are of 45 each and the other two opposing angles ate of 135" each; an arrangement of 14 elements composed of thirty-two fUndamental unit-triangles.

7 A didactic assembly according to Claim 6, wherein that each element be coloured in one of twelve specified colours, the specified colours providing a restricted colour wheel of both spectral and non-spectral colours within the visible wavelengths. This restricted, specified colour wheel ranges from red through orange to yellow, through green to cyan blue, through purple and violet to magenta and so back to red These shaped elements are coloured with one of the colours specified as follows:

Colour NCS Wavelength PANTONE Q CIE (Sweden) in nm Color ) .) y( > ) 1 Red 1080 R 620 P199 0.5372 0.3074 3 Orange 0090 YSOR 590 P151 0.5432 0.4018 5 Yellow 0080 Y 575 P109 0.4524 0.481 7 Lime 0080 G40Y 562 P374 0.3703 0.5204 9 Green 2070 G 508 P3415 0.2322 0.4236 11 -Drine 2060 BOG 489 P320 0.202 0.3025 13 Cyan 1070 B 481 P299 0.1813 0.2223 15 Cobalt blue R83B 470 P293 0.1834 0.1388 17 Blue-violet 4050 R50B 430 P259 0.2500 0.1800 19 Purple R40B -530 P246 0.3407 0.2216 21 Magenta R30B -507 Pantone RlDdamine Red 0.3795 0.2304 23 Raspberry R20B 496 P214 0.4392 0.2674 25 leead-grey 6010 R70B Fieldgrey 7010 G1OY In lieu of colours described in this Patent, you may use the PANTONE s Colors above. the standards for which are shown in the curent edition of the PANTONE Color Guide 1000.

*PANTONE Q9 is a registered trademark of Pantone. Inc.

8 A didactic assembly according to Claim 1 to 7, wherein the thickness of the elements is determined to be no greater than a proportion of three tenths (3/10 or 0.3) of the unit-length and the minimum thickness may be determined by the material of construction.

9 Shaped and coloured elements according to Claims 1 to 8 which may be used as physical illustration of a scheme of colour theory and description, devised by the patentee (text available from invention on request).

10 Shaped and coloured elements according to Claims 1 to 8 which may be used to further understanding of mathematical proportion and area.

11 Shaped and coloured elements according to Claims 1 to 8 which may be used in a computer programme to facilitate manipulation of the position size. shape and colour of the said elements in the development of surface designs and in the exploration and demonstration of colour theory.

12 A didactic assembly according to Claims 1 to 5 and to Claim 8, wherein a tray or framed board is provided with the elements, the tray being, within the raised border, of planar dimensions 5 unit-lengths by 5 unit-lengths. The tray may be of suitable materials complimentary to the invention claimed herein, as may its other dimensions.

13 A didactic assembly according to Claim 12 characterisedby the said elements being magnetic and by the base of the said tray or framed board being made of suitable metal material.

14 A didactic assembly according to any of the preceding Claims characterised by the sizes of the elements being further inter-related to specified colours or to specified groups of colours.

15 A didactic assembly according to any of the preceding Claims wherein the elements of triangular, rectilinear or lozengal form may be placed side by side to form a tessellated assembly.

16 A didactic assembly according to any of the preceding Claims wherein the elements may be sorted according to the various shapes and colours of which they comprise.

17 A didactic assembly according to any of the preceding Claims wherein, while the elements are provided in a basic set of twenty-four shapes, there are other combinations of elements available to extend or vary the basic set.

18 A didactic assembly according to any of the preceding Claims which may be used as a designer's tool to aid the generation of patterns, logotypes and other planar designs.

19 A didactic assembly according to any of the preceding Claims which may be used as an educational toy.

20 A didactic assembly according to any of the preceding Claims which may be used as an executive toy.

21 A didactic assembly according to any of the preceding Claims which may be used as a mathematical puzzle.

22 A didactic assembly according to any of the preceding Claims which may be used as a work of art or aesthetic decorative object, capable of being used to make further aesthetic decorative objects.

23 A 'set' comprising shaped and coloured elements according to Claims 1 to 5, a computer programme according to Claim 11 and a tray according to Claim 12 or according to Claims 12 and 13, which together with an explanatory book or booklet may describe the historical and theoretical background to the specified colour theory, as well as the historical origins of the shaped blocks and suggestions and advice for use of the elements and the computer programme.

24 A 'set' according to any of the preceding Claim 23 which may be used as a designer's tool to aid the generation of patterns, logotypes and other planar designs.

25 A 'set' according to any of the preceding Claim 23 which may be used as an educational toy.

26 A 'set' according to any of the preceding Claim 23 which may be used as an executive toy.

27 A 'set' according to any of the preceding Claim 23 which may be used as a mathematical puzzle.

28 A 'set' according to any of the preceding Claim 23 which may be used as a work of art or aesthetic decorative object, capable of being used to make further aesthetic decorative objects.

29 A didactic assembly according to any of the preceding Claims wherein any novel colouring or selfcolouring or combination including colouring herein disclosed in the foregoing specification or claims and shown in the drawings or shown in the drawings, whether or not within the scope of or relating to the same invention as any of the preceding claims.

30 A didactic assembly substantially as herein described with reference to, and illustrated by, the accompanying drawings.