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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'…
Palindromes
Palindromes are achiral words, such as: - nun - madam - pop Or achiral phrases (once spaces and punctuation are removed, by convention) such as these famous examples: - Nurses, run! - Madam, I'm Adam! - A man, a plan, a canal: Panama! Or achiral sequences, such as a palindromic…
Penrose Tiles
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling ... - Wikipedia: Penrose tiling Yeh yeh yeh we know all that. APERIODIC No repeating period. Get this -- it's true chaos.…
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
**warning Once you learn about the Reuleaux Triangle you may start to see it everwhere! In buildings, in coffee tables, in kids playground equipment, in beer logos... Reuleaux Rules Our World!** Ever wanted to drill a square-hole? Is it possible to build a drillbit that would p…
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…
Sierpinski Triangle
Anything that's covered here is almost definitely covered in a very well known webpage, The Sierspinski Triangle Page to End Most Sierspinski Triangle Pages but regardless, I must press on. Let's draw a triangle. to triangle :length fd :length lt 120 fd :length lt 120 fd :…
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…
Triangle
I wanted to draw a triangle, so I sat down on the ground and thought about it for a while. When it all comes down to it. What it is, you see. How it works. Well a triangle has. It has 3. - 3 points. - 3 corners. - 3 angles. It's 3 lines really. So I want to draw 3 lines. The …
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