Where in the World Isn't Bob Saget?

Lucky

Well-Known Member
Once in a kingdom far, far away, a beautiful girl was born to a king & queen. The castle in which she was born was a structure to behold. The diagonals of the side walls divide each other into segments with lengths that are pairwise equal; in terms of the picture below, AE = DE, BE = CE (and AECE if one wishes to exclude rectangles). Opposite angles are supplementary, which in turn implies that isosceles trapezoids are cyclic quadrilaterals, at least according to the fairy godmother who helped construct the magical castle.
But a jealous witch wanted to destroy the kingdom, and she knew too well that the castle would only fall if the ratio in which each diagonal is divided is equal to the ratio of the lengths of the parallel sides that they intersect, that is,

76a1526fd998b6ecea6d7c5b6cb06c20.png

The length of each diagonal is, according to Ptolemy's theorem, given by

5a1a8b58d93b1517f8cd1af8f7f93be1.png

where a and b are the lengths of the parallel sides AD and BC, and c is the length of each leg AB and CD.

But luckily the witch miscalculated her assault, and the young princess & her kingdom lived happily ever after.

I have my FPs for "Storytime With Belle and Pythagoras." :cool:
 

trr1

Well-Known Member
September 26

National Dumpling Day*
National Pancake Day
National Johnny Appleseed Day
National Shamu the Whale Day
National Hunting and Fishing Day – Fourth Saturday in September
National Family Health and Fitness Day USA – Last Saturday in September
National Public Lands Day – Usually Last Saturday in September September 26, 2015
 

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