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We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are commensurable. (a) Construct with ruler and compass any rectilinear planar figure (other than a square) that exhibits two incommensurable magnitudes. Label these magnitudes. (b) Demonstrate why the magnitudes you have labelled cannot have a common divisor (you may use modern knowledge of number in your demonstration).

We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are commensurable. (a) Construct with ruler and compass any rectilinear planar figure (other than a square) that exhibits two incommensurable magnitudes. Label these magnitudes. (b) Demonstrate why the magnitudes you have labelled cannot have a common divisor (you may use modern knowledge of number in your demonstration).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.1: Congruent Triangles
Problem 7E: In ABC, the midpoints of the sides are joined. a what does intuition suggest regarding the...
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(5) We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are commensurable. (a) Construct with ruler and compass any rectilinear planar figure (other than a square) that exhibits two incommensurable magnitudes. Label these magnitudes. (b) Demonstrate why the magnitudes you have labelled cannot have a common divisor (you may use modern knowledge of number in your demonstration).
Transcribed Image Text:(5) We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are commensurable. (a) Construct with ruler and compass any rectilinear planar figure (other than a square) that exhibits two incommensurable magnitudes. Label these magnitudes. (b) Demonstrate why the magnitudes you have labelled cannot have a common divisor (you may use modern knowledge of number in your demonstration).
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