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Apollonian Construction Problem [03/06/2001]

Given a line and two points A and B, construct a circle tangent to the line and containing the two points.

Apollonius' Problem [09/07/2000]

Given three circles, is it possible to construct a circle tangent to each of them using only a compass and straightedge?

Classical Geometry [04/16/2002]

Let ABC be a triangle with sides a, b, c. Let h be the perpendicular from A to a, and m the median from A to the midpoint of a. Construct the triangle using only ruler and compass if you know A, h, m.

Constructing a Segment of a Given Length [09/09/2005]

How do you construct a segment of length "the 8th root of 3" using a compass and a straightedge?

Constructing a Triangle [09/29/2003]

Let x be a given angle. Let m and n be given lengths such that n > m. How can I construct triangle ABC such that AB = m, AC + CB = n, and the measure of angle ACB = x?

Constructing the Trisection of an Angle [07/20/2008]

Why can you construct the trisection of some angles and not of others?

Drawing Regular N-gons (Compass and Straightedge) [11/17/1997]

Is it true that the only regular n-gons that can be drawn using ONLY a straightedge and compass are those with the number of sides equal to a Fermat Prime or a product of Fermat Primes?

Inconstructible Regular Polygon [02/22/2002]

I've been trying to find a proof that a regular polygon with n sides is inconstructible if n is not a Fermat prime number.

Triangle Construction [03/11/2002]

Let ABC be a triangle with sides a, b, c. Let r be the radius of the incircle and R the radius of the circumcircle. Knowing a, R, and r, onstruct the triangle using only ruler and compass.

Trisecting an Angle [11/21/1996]

Is there a proof that you can't trisect an angle?

Trisecting a Pizza [05/13/2002]

Without the use of a ruler, protractor or other measuring device, is there a simple way to divide a pizza into 3 equal sized slices?

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