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Shaun Crampton
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<rant>Just had to download a PDF form, fill it in in Acrobat reader and then upload it TO A WEB FORM.  Who could have possibly thought that was a good idea?

If that wasn't bad enough, Acrobat reader has a bug where it only saves the filled in values if you use the "Save" option, not "Save as..." (lost all my entered data to this) and "Save" saves over the original document even if you've done a "Save as..." since you opened it (lost my previous version of the form to this).</rant>

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Prime factorizations of small numbers, by John Graham-Cumming

The Fundamental Theorem of Arithmetic states that every natural number greater than 1 can be expressed as a product of prime numbers, and that the product is unique up to changing the order of the factors. For example, the number 12 can be expressed as 2x2x3, or as 2x3x2, or as 3x2x2, where 2 and 3 are prime numbers. These factorizations are all rearrangements of each other, and there are no other ways to write 12 as a product of prime numbers.

This picture by John Graham-Cumming shows the factorizations into primes of the numbers from 2 to 100. Note that the circle representing 1 is blank, because 1 is not prime: if we allowed 1 to be prime, then we would have 12=2x2x3=1x2x2x3, which would break the Fundamental Theorem of Arithmetic.

The picture comes from an April 2012 blog post by Graham-Cumming, which you can find here: http://blog.jgc.org/2012/04/make-your-own-prime-factorization.html. In the post, he provides links to source code that you can use to generate similar pictures for yourself. There is also a link to order this picture on a T-shirt.

The Fundamental Theorem of Arithmetic appears in Volume VII of Euclid's 13-volume treatise Elements, which he wrote around 300 BC. Wikipedia has more information about the theorem here: http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic.

(Found via Clare Sealy on Twitter.)

#mathematics

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How to get AVR-libc's floating point support to play nice with Eclipse.  Needed this for the new revision of my ArduRoller balance bot.

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Hoodoos, Bryce Canyon, Utah, USA.
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Labyrinth 
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One for +Katie Boswell 
I wish you all a Merry Christmas, a peaceful day with the persons you love and, preferably, with lots of mushrooms :) 
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Mushrooming in San Francisco's Presidio park. #mushrooms   #photography   #macro  
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2014-12-22
15 Photos - View album

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Panamint Dunes, Death Valley
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