The Lily Problem Puzzle

Insight: The Lily is the radius of a circle, of which the pond bottom is the diameter.

1. Whenever two lines intersect in a circle, the product of the parts of one line equal the product of the parts of the other. (Euclid III.35)

AD x DF = BD x DE
10 x DF = 21 x 21 (441)
DF (lower part) = 44.1

2. DF + 10 = 54.1 (diameter)
AC = 27.05 (radius)

3. DC = 27.05 - 10

Pond depth is 17.05

Euclid, a student of Plato’s writings living in Alexandria around 300 BC, collected into his book The Elements, all the geometry theorems that were current at that time. In the process he also established the rigorous way such theorems were proved. Given this, therefore that. Q.E.D. Asked by the younger Archimedes if there was no easier way to understand the nature of squares and circles, the old man famously replied: “There s no royal road to geometry.” Students have been sighing over that for 2000 years.

Here's a puzzle you can do on your own, invented by Richard Feynman (Nobel Prize for Physics) when he was in high school. Go to the nearest flagpole and pull the bottom of the rope (CD) away from the pole as far as you can. Measure the difference between B and the ground and D and the ground. Now measure the horizontal distance between the bottom of the rope (A) and the pole (B). So, knowing AD and AB, how tall is the flag pole (BC)?

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