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Exercise 1. Which proposition of the Elements implies that the angle 60° is constructible?

Exercise 1. Which proposition of the Elements implies that the angle 60° is constructible?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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please solve all questions ?? ? euclidean geometry
Exercise 1. Which proposition of the Elements implies that the angle 60° is constructible? Exercise 2. Which proposition, if any, of the Elements implies that every angle can be bisected? Which proposition, if any, implies that every angle can be trisected? Exercise 3. Prove that if is constructible, then so are 0/2 and 20. What about 8/3 and 30? Exercise 4. Is it true that if the regular n-gon is constructible, then so is the regular 2n-gon? Exercise 5. Which regular n-gons are constructible according to Book I of Euclid's Elements? Exercise 6. Prove that the angle 15° is constructible.
Transcribed Image Text:Exercise 1. Which proposition of the Elements implies that the angle 60° is constructible? Exercise 2. Which proposition, if any, of the Elements implies that every angle can be bisected? Which proposition, if any, implies that every angle can be trisected? Exercise 3. Prove that if is constructible, then so are 0/2 and 20. What about 8/3 and 30? Exercise 4. Is it true that if the regular n-gon is constructible, then so is the regular 2n-gon? Exercise 5. Which regular n-gons are constructible according to Book I of Euclid's Elements? Exercise 6. Prove that the angle 15° is constructible.
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