# Category: geometry

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### Chirality

Chirality, pronounced as if the "ch" is a "k"... where was I, chirality. Your nose is not chiral. Your hands are chiral. Each of your feet is chiral. But taken as a pair, they are no longer chiral. A donut is not chiral. A threaded screw is chiral. A water molecule is not chira…

### Girih Tiles

Girih Tiles are a set of five tiles that give rise to complex and beautiful geometric patterns. They originated in Islamic architecture. See Also - Penrose Tiles External Links - Wikipedia: Girih Tiles - Girih Editor…

### Harriss Spiral

Few spirals are as beautiful as the Harriss spiral. to curve :length pu lt 45 fd :length/2 * sqrt(2) rt 90 pd penwidth :length/15 arc :length/2 * sqrt(2) 90 pu fd :length/2 * sqrt(2) lt 90 lt 45 rt 90 pd end to harriss :length :limit if :length > :limit [ color [200…

### Higher Dimensions

The universe that we experience is 3 Dimensional, or, if you treat time as a limited dimension, 4 Dimensional. There's a famous novella entitled "Flatland: A romance of Many Dimensions" primarily concerned with life in a 2-Dimensional universe, but also covering a 2-Dimensional …

### Mobius Strip

Album cover for 'The Infinite Road' by Toyz External Links - Album cover for 'The Infinite Road'…

### Penrose Tiling

A famous non-repeating tiling pattern, invented (discovered.) by Roger Penrose, a giant in the worlds of mathematics and floor-coverings. The following logo program produces a penrose tiling. I found this at http://logo.twentygototen.org/E3_yJcQ4. I haven't looked through it en…

### Penrose Triangle

"Mr Escher's office please" "Up the stairs, keep turning right" —@MooseAllain In Real Life Cartoon —New Yorker Cartoon By Robert Leighton Logo Version to piece :size lt 60 fd :size lt 120 fd (3* :size) lt 120 fd (4 * :size) lt 60 fd (1* :size) lt 120 fd (3* :size)…

### Polygon

I remember a maths teacher saying to me, "It's amazing how clear it is, when you use Logo, that a circle is just a polygon with an infinite amount of sides" In that spirit, here's a simple formula for a polygon. Repeat {sides}: Forward {length}, Right Turn 360/{sides}. I tried …

### Reuleaux Triangle

Ever wanted to drill a square-hole? Is it possible to build a drillbit that would produce such a shape? It seems impossible, but how impossible is it? Can we drill holes that are any shape other than circular? A circle is a curve of constant width. As you rotate a circle its wi…

### Sierpinski Polygon

A Sierpinski triangle is the result of this line of thinking: To draw a Sierpinski triangle just draw three smaller Sierpinski triangles. (Unless the shape is too small... then just draw a regular triangle). What if we make the number 3 a parameter, :side, so that we create Sie…

### Spirals

Swirls and spirals appear in nature in all kinds of places. In the seeds of a sunflower, in the vortex of a hurricane, in the horns of a goat, in the shell of a snail, in the curling fronds of a fern, in this guy's beard. . In this totally naturally occurring jetty: Spirals in…

### Square-Cube Law

If two items are structurally identical in all aspects except size, then the smaller item will have a greater proportion of area to volume, both in terms of surface area and cross-sectional area. External Links - secretGeek.net: The Principle of Scale - Wikipedia: Square Cube La…

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