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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,
construct 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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