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The Euler Brick Problem
11
Transcript
Concepts Used to Find Solution:
Who was Euler?
The smallest Euler Brick
Leonhard Euler (Oy-ler) is a famous Swiss mathematician.
- Born in Basel, Switzerland on April 15, 1707
- Married to Katharina Gsell
- Lost sight in 1740
- The smallest primitive Euler Brick was discovered by Paul Halcke a German mathemetician in 1719.
- The dimensions of this Euler brick is: (a, b, c) = (44, 117, 240) and face diagonals (d, e, f ) = (125, 244, 267).
https://www.usna.edu/Users/math/meh/euler.html
What is the Euler Brick Problem?
- The Euler brick problem is an unsolved question posed by Leonhard Euler.
- It asks if it is possible for there to be a rectangular solid such that all lengths and diagonals are integers?
http://distributed.org.ua/forum/index.php?showtopic=6144&st=0
Do you believe a perfect Euler Brick Exists?
Examples:
- If (a, b, c) is a solution, then (ka, kb, kc) is also a solution for any k. Given an Euler brick with edge-lengths (a, b, c), the triple (bc, ac, ab) is an Euler brick as well.
- At least two edges of an Euler brick will be divisible by 3.
- At least two edges of an Euler brick will be divisible by 4.
- At least one edge of an Euler brick will be divisible by 11.
Height Width Length
85 132 720
117 44 240
231 160 792
275 240 252
351 132 720
693 140 480
825 720 756
Pythagorean Quadruples
a^2 + b^2 +c ^2 = d^2
The Euler Brick Problem
by Etienne Batiste and Chloe Tate
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