You are currently browsing the tag archive for the ‘area’ tag.

My colleague Ricardo Pérez-Marco showed me a very cute proof of Pythagoras’ theorem, which I thought I would share here; it’s not particularly earth-shattering, but it is perhaps the most intuitive proof of the theorem that I have seen yet.

In the above diagram, a, b, c are the lengths BC, CA, and AB of the right-angled triangle ACB, while x and y are the areas of the right-angled triangles CDB and ADC respectively. Thus the whole triangle ACB has area x+y.

Now observe that the right-angled triangles CDB, ADC, and ACB are all similar (because of all the common angles), and thus their areas are proportional to the square of their respective hypotenuses. In other words, (x,y,x+y) is proportional to (a^2, b^2, c^2). Pythagoras’ theorem follows.

Read the rest of this entry »

Archives

RSS Google+ feed

  • An error has occurred; the feed is probably down. Try again later.
Follow

Get every new post delivered to your Inbox.

Join 3,780 other followers