Classical Geometries] How do you solve this? 1. A straight line may be drawn between any two points. 2. Any terminated straight line may be extended indefinitely. 3. A circle may be drawn with any given point as center and any given radius. 4. All right angles are equal. A previous example include creating an equilateral triangle from two intersecting circles. Is there an axiom that is not justified when contructing this triangle?

Classical Geometries] How do you solve this? 1. A straight line may be drawn between any two points. 2. Any terminated straight line may be extended indefinitely. 3. A circle may be drawn with any given point as center and any given radius. 4. All right angles are equal. A previous example include creating an equilateral triangle from two intersecting circles. Is there an axiom that is not justified when contructing this triangle?

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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Question

[Classical Geometries] How do you solve this?

1. A straight line may be drawn between any two points.
2. Any terminated straight line may be extended indefinitely.
3. A circle may be drawn with any given point as center and any given radius.
4. All right angles are equal.

A previous example include creating an equilateral triangle from two intersecting circles. Is there an axiom that is not justified when contructing this triangle?

2.
Review the three
constructions/proofs you have done previously,
is (are) there any step(s) that is(are) not justified by the axiomatic system
of Euclid?

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