Monday, May 4, 2009

Elegant Solution


A geometry problem called for finding an unknown angle EOD. My son approached it steadily and safely:

< AOC = <AOB – <COB = 180° -125° = 55°
<EOD = <AOB – (<AOE + <DOB) = 180° – (40° + 55°) = 85°

I asked him to look for another way of solving this problem. This time after finding angle AOC he came up with 360° – 125° – 40° - 55°X2 = 85° , which essentially is a variation on the first method.

“Try something different”, I kept insisting.

After a bit of hesitation he found it.

<COB and <AOD are vertically opposite angles and therefore
125° – 40° will give us the answer!!

Only after he wrote it down I realized how graceful and succinct this solution is - the epitome of elegance.

<EOD = <AOD – <AOE = 125° – 40° = 85°

What a beauty!

*Why doesn't blogger support the symbol for angles? I had to substitude with "<" instead, which looks slightly odd.

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