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[[File:Golden gnomom.jpg|frame|300x250px|Golden gnomom]] <br>
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[[File:Golden gnomom.jpg|frame|300x250px|Golden gnomon]] <br>
 
<small> [https://en.wikipedia.org/wiki/Golden_triangle_(mathematics) Wikipedia] </small>
 
<small> [https://en.wikipedia.org/wiki/Golden_triangle_(mathematics) Wikipedia] </small>
 
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The golden gnomon is another isosceles triangle where a ratio between one of the identical sides <math> a </math> and the base <math> b </math> is the reciprocal of the golden ratio <math> \frac{1}{\phi} </math>.
  
 
Regarding Penrose tiling, a golden triangle and two golden gnomons make up a regular pentagon, which ties in with the golden ratio local pentagon symmetry discussed earlier.
 
Regarding Penrose tiling, a golden triangle and two golden gnomons make up a regular pentagon, which ties in with the golden ratio local pentagon symmetry discussed earlier.

Latest revision as of 01:11, 7 December 2020

Robinson Triangles

Robinson triangles, also known as golden triangles due to their close relation with the golden ratio discussed previously, make up the spikes of regular pentagrams.

Pentagram

Wikipedia

A golden triangle is an isosceles triangle where a ratio between one of the identical sides $ a $ and the base $ b $ is the golden ratio $ \phi $.

$ \frac {a}{b} = \phi $
Golden triangle

Wikipedia

A similar triangle to the Robinson triangle is the golden gnomon:

Golden gnomon

Wikipedia

The golden gnomon is another isosceles triangle where a ratio between one of the identical sides $ a $ and the base $ b $ is the reciprocal of the golden ratio $ \frac{1}{\phi} $.

Regarding Penrose tiling, a golden triangle and two golden gnomons make up a regular pentagon, which ties in with the golden ratio local pentagon symmetry discussed earlier. P2 Penrose tiling are made from kites and darts. A kite is made from two golden triangles, and a dart is made from two gnomons.

Further Readings:

One final note – if you like proofs, you will enjoy this site: http://mrbertman.com/penroseTilings.html. It contains many definitions and theorems that deal with how to place a tile correctly (the site uses the term “legally”) and why those rules exist. You can even create your own Penrose tiling!


Penrose Tiling Home

Previous Section: Golden Ratio

Next Section: Real World Examples

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