An Euler Brick is an a × b × c cuboid where the dimensions a, b, c are positive integers, as are the diagonals of each face. The first, (44, 117, 240), was discovered in 1719 by Paul Halcke. (a) Write a function IsItEuler(triplel, triple2) which accepts as input two tuples representing distinct Pythagorean triples and returns True if together they describe two faces of an Euler Brick, and False otherwise. For example the inputs (44, 117, 125), (117, 240, 267) should return True, as should (117,240,267), (117, 44, 125), etc.. (b) Write a function Bricks (n) to return a list of Euler bricks (a, b, c) where 0 < a < b

Database System Concepts
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Chapter1: Introduction
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An Euler Brick is an a × b × c cuboid where the dimensions a, b, c are positive integers, as are the diagonals
of each face. The first, (44, 117, 240), was discovered in 1719 by Paul Halcke.
(a) Write a function IsItEuler(triplel, triple2) which accepts as input two tuples representing
distinct Pythagorean triples and returns True if together they describe two faces of an Euler Brick, and
False otherwise. For example the inputs (44,117,125),(117,240,267) should return True, as should
(117,240,267), (117,44,125), etc..
(b) Write a function Bricks (n) to return a list of Euler bricks (a, b, c) where 0 < a <b<c<n.
Hint: Use your functions Pyth and IsItEuler.
(c) How many Euler bricks are there with all dimensions < 1000? How many of them are primitive? Write
your answer as a comment, explaining what a "primitive" Euler brick is.
Transcribed Image Text:An Euler Brick is an a × b × c cuboid where the dimensions a, b, c are positive integers, as are the diagonals of each face. The first, (44, 117, 240), was discovered in 1719 by Paul Halcke. (a) Write a function IsItEuler(triplel, triple2) which accepts as input two tuples representing distinct Pythagorean triples and returns True if together they describe two faces of an Euler Brick, and False otherwise. For example the inputs (44,117,125),(117,240,267) should return True, as should (117,240,267), (117,44,125), etc.. (b) Write a function Bricks (n) to return a list of Euler bricks (a, b, c) where 0 < a <b<c<n. Hint: Use your functions Pyth and IsItEuler. (c) How many Euler bricks are there with all dimensions < 1000? How many of them are primitive? Write your answer as a comment, explaining what a "primitive" Euler brick is.
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