REPEAT PATTERNS - #6-7 SYMMETRY - #8-9 BLUE PRINT - #10-11 THE GOLDEN SECTION - #12-13 FRACTALS - #14-15 GRIDS - #16-17

GEOMETRY DESIGN VOL.1

CONTENTS

SPIROGRAPHS - #4-5

A piece of equipment which is used to draw intricate curved patterns using interlocking plastic cogs and toothed rings of different sizes. A Spirograph is a geometric drawing toy that produces mathematical roulette of curves. It was developed by British engineer Denys Fisher and first sold in 1965. The original US-released Spirograph consisted of two differentsized plastic rings, with gear teeth on both the inside and outside of their circumferences. They were pinned to a cardboard backing with pins, and any of several provided gearwheels, which had holes provided for a ballpoint pen to extend through them to an underlying paper writing surface. It could be spun around to make geometric shapes on the underlying paper medium. Later, the SuperSpirograph consisted of a set of plastic gears and other interlocking shapesegments such as rings, triangles, or straight bars. It has several sizes of gears and shapes, and all edges have teeth to engage any other piece. For instance, smaller gears fit inside the larger rings, but also can engage the outside of the rings in such a fashion that they rotate around the inside or along the outside edge of the rings.

SPIROGRAPHS 4

GEOMETRY DESIGN VOL.1

5

Repeat patterns are also known as translation patterns and are rigid elements where the motif is simply repeated over and over again along a horizontal and vertical line. These elements normally repeat in a predictable manner. Repeat structures are a crucial element of pattern design , they constitute one method of organization used is many areas of design that are concerned with ornamentation. Such structures enable a design to be extended in any direction to create an uninterrupted pattern. Pattern is potentially infinite , and a well designed pattern always gains by repetition. Design exists not as a single motif/ unit or picture that is merely reproduced, but as a continuous repeating pattern. Artists have always used geometrical principles and forms recognizing the value of balance , harmony , geometrical precision and symmetry. The design will be more effective as repeating unit if it is asymmetrical.

REPEAT PATTERNS 6

GEOMETRY DESIGN VOL.1

7

The type of symmetries that are possible for a geometric object depend on the set of geometric transforms available and what object properties should remain unchanged after a transform. Because the composition of two transforms is also a transform and every transform has an inverse transform that undoes it, the set of transforms under which an object is symmetric form a mathematical group.

SYMMETRY

Symmetry is an exact mathematical patterned self-similarity that can be demonstrated with the rules of a formal system, such as geometry or physics. The most familiar type of symmetry for many people is geometrical symmetry. A geometric figure has symmetry if there is an isometry that maps the figure onto itself

YRTEMMYS

Symmetry is the identical reflection of two sides. In order to be symmetrical, the right side of the pattern or object is exactly the same as the left side of the pattern or object.

Reflectional symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.

8

GEOMETRY DESIGN VOL.1

9

A blueprint is a reproduction of a technical drawing, documenting an architecture or an engineering design, using a contact print process on lightsensitive sheets. Introduced in the 19th century, the process allowed rapid and accurate reproduction of documents used in construction and industry. The blue-print process was characterized by light colored lines on a blue background, a negative of the original. The process was unable to reproduce color or shades of grey. Various base materials have been used for blueprints. Paper was a common choice; for more durable prints linen was sometimes used, but with time, the linen prints would shrink slightly.

10

BLUE PRINT The designs created to show where i phone icons are to be placed are originally mocked up in blue print.

GEOMETRY DESIGN VOL.1

11

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.’ In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b,The golden ratio is also called the golden section or golden mean. Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into “extreme and mean ratio” (the golden section) is important in the geometry of regular pentagrams and pentagons

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THE GOLDEN SECTION

GEOMETRY DESIGN VOL.1

13

A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature. A fractal is a mathematical set that typically displays self-similar patterns, which means it is “the same from near as from far”. Fractals may be exactly the same at every scale, or, they may be nearly the same at different scales. The concept of fractal extends beyond self-similarity and includes the idea of a detailed pattern repeating itself. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. Doubling the edge lengths of a square scales its area by four, which is two to the power of two, because a square is two dimensional. Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two to the power of three, because a sphere is three-dimensional. If a fractal’s one-dimensional lengths are all doubled, the spatial content of the fractal scales by a number which is not an integer. A fractal has a fractal dimension that usually exceeds its topological dimension and may fall between the integers.

FRACTALS

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GEOMETRY DESIGN VOL.1

15

A grid is evenly divided and equally spaced squares on a figure or flat surface. A grid is put in place to make sure content is spaced accurately and follows a structure. In graphic design, a grid is a structure made up of a series of intersecting straight vertical, horizontal, and angular or curved guide lines used to structure content. The grid serves as an armature on which a designer can organize graphic elements images, glyphs, paragraphs in a rational, easy to absorb manner. A grid can be use to organize graphic elements in relation to a page, in relation to other graphic elements on the page, or relation to other parts of the same graphic element or shape. Grids are also used in web design. Some grid systems specify fixed-width elements with pixels, and some are â€˜fluidâ€™, meaning that they call for page element sizing to be in relative units like percentages, rather than absolute units like pixels or points.

GRIDS

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GEOMETRY DESIGN VOL.1

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GEOMETRY DESIGN VOL.1

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