Here are two ways to draw a disc:

• Make a circle and fill it in
• Draw a bunch of rings with a thick marker

The amount of “space” (area) should be the same in each case, right? And how much space does a ring use?

Well, the very largest ring has radius “r” and a circumference 2 * pi * r. As the rings get smaller their circumference shrinks, but it keeps the pattern of 2 * pi * current radius. The final ring is more like a pinpoint, with no circumference at all.

Now here’s where things get funky. Let’s unroll those rings and line them up. What happens?

• We get a bunch of lines, making a jagged triangle. But if we take thinner rings, that triangle becomes less jagged (more on this in future articles).
• One side has the smallest ring (0) and the other side has the largest ring (2 * pi * r)
• We have rings going from radius 0 to up to “r”. For each possible radius (0 to r), we just place the unrolled ring at that location.
• The total area of the “ring triangle” = 1/2 base * height = 1/2 * r * (2 * pi * r) = pi * r², which is the formula for area!

Yowza! The combined area of the rings = the area of the triangle = area of circle!

This was a quick example, but did you catch the key idea? We took a disc, split it up, and put the segments together in a different way. Calculus showed us that a disc and ring are intimately related: a disc is really just a bunch of rings.

http://betterexplained.com/articles/a-gentle-introduction-to-learning-calculus/

1. Jigme Khesar Namgyel Wangchuck — King of Bhutan

2. Michaelle Jean — Governor General of Canada

3.  Barack Obama — I can’t believe he lost to fucking Lukashenko

4. Mohammed VI — King of Morocco

5. Moussa Dadis Camara — President of the Republic of Guinea’s National Council for Democracy and Development

6. Cristina Fernandez de Kirchner — President of Argentina

7. Xanana Gusmao — Prime Minister of East Timor (aka Silver Fox)

8. Pierre Nkurunziza — President of Burundi

9. Qaboos bin Said al Said — Sultan of Oman

10. He didn’t appear at all on hottestheadsofstate.com, but this is my version, and I say Tibet IS a country!

His Holiness the 14th Dalai Lama

]]> http://mixnmingle.wordpress.com/2010/05/12/hottest-heads-of-state-imho/feed/ 0 rosmigel dalai-lama-1959 http://mixnmingle.wordpress.com/2010/05/11/i-love-art/ http://mixnmingle.wordpress.com/2010/05/11/i-love-art/#comments Tue, 11 May 2010 19:56:19 +0000 rosmigel http://mixnmingle.wordpress.com/?p=155 ]]> none of these are photoshopped, by the way

and now you can seriously run on water . . . I remain skeptical about this, but I still am captivated by this video

if you’re interested in more, here’s their blog: http://www.liquidmountaineering.blogspot.com/

blackpeopleloveus.com