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Two questions for you:

The first is more mundane, and is about compass and straight edge construction:

A. Quickest, cleanest way to construct a regular octagon.

B. Given a side, quickest, cleanest way to raise a regular octagon on it.

The second:

Where would you cut a unit square to create a regular octagon? (how far from the corner is your first cut?)

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3 Comments leave one →
1. September 6, 2008 am30 2:17 am 2:17 am

I really can’t think of anything for A and B other than what seems obvious:

A. in a circle, diameter, contruct perpendicular diameter, angle-bisect diameters one way and you’re basically done.

B. I can think of nothing good here but to bite the bullet and start contructing 45 degree angles at the ends. I’m sure there must be something better but it’s not coming to me.

2) side a, cut in by $\frac{2-\sqrt{2}}{2}a$. Simple argument from proportion and Pythagoras.

2. Anonymous permalink
November 10, 2008 am30 2:54 am 2:54 am

4.2

3. Anonymous permalink
November 30, 2008 pm30 3:35 pm 3:35 pm

The method I use to draw a regular octogon:
1. Start with a straight line.
2. Complete a 90 degree bisect.
3. Draw 4 angle bisects on each of the 4 90 degree angles that you’ve created.
4. Place the point of you compass at the mid-point where all the lines meet.
5. Draw a circle, it’s circumference must cross all of the lines coming from the mid-point.
6. Using a straight edge connect each line (where it is crossed by the circle) to the next along.
7. When all 8 lines are drawn you have a circle.
8. It seemed appropriate to have an ‘8’ for this answer.