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A Quick Geometric Problem

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Michael Penn put this up on his YouTube channel earlier today, and it is indeed an elegant little problem. Here it is


Michael Penn solves this using congruent triangles, the angle sum of a triangle (180 °) and angles on a straight line (180 °). α is always 60 °, whatever the length of AD and CE. It's not that obvious and I was quite surprised.

However thinking about it later, I saw we can solve the problem using symmetry and the solution is super-nice. Here's how - just add a third line.



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Snowflakes again

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Edited by Richard Walker, Saturday, 23 Jan 2010, 01:53

I've always thought symmetry was heart-breaking and snowflake patterns marvellous in their variety - and their temporary existence.  Bentley, the New England farmer who photographed so many snow crystals over 40 years (see earlier blog post snowflake(1)) lamented that each was unique and so beautiful, but gone forever in seconds or less.

Yesterday some of Bentley's original photos - plates I guess - were at auction and this was reported in many newspapers.  Go look

 

 

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A feeling for snow

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Edited by Richard Walker, Tuesday, 5 Jan 2010, 00:05

Miss Smilla's Feeling for Snow is a famous novel.  But Wilson Bentley also had a feeling for snow and was the pioneer of snowflake photography, see

http://en.wikipedia.org/wiki/Wilson_Bentley

A more recent photographer of snow crystals is Kenneth Libbrech, see

 

http://www.newscientist.com/gallery/dn16170-snowflakes/5

These images are all wonderful.

Looking at snowflakes many have asked how each of the six arms of the snowflake 'knows' how to keep itself in symmetry.

 

 

Permalink 4 comments (latest comment by Richard Walker, Saturday, 23 Jan 2010, 01:48)
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