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For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB -CD. A 23

For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB -CD. A 23

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB - CD. D, A B %23
Transcribed Image Text:For the next few problems, suppose we are operating under Saccheri's Hypothesis of the Acute Angle (HAA). That is, we suppose that the congruent summit angles of any Saccheri Quadrilateral are acute. The thrust of these problems is to prove (1) that under HAA, triangles have fewer than 180° and (2) that under HAA the Pythagorean relationship between hypotenuse and legs of a right triangle cannot hold. This development is taken from Richard Trudeau's The Non-Euclidean Revolution. Under HAA, prove that if ABCD is a Saccheri Quadrilateral as shown, then AB - CD. D, A B %23
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