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Browse High School Constructions
Stars indicate particularly interesting answers or
good places to begin browsing.
 Drawing a Circle Tangent to an Angle [05/13/2000]

Given an angle and any point inside it not on its bisector, how can you
draw a circle that goes through the point and is tangent to both sides of
the angle with just a compass and protractor?
 Drawing An Ellipse [11/24/1997]

How do you draw an ellipse with only a straight edge and a compass?
 Drawing Diagrams [08/02/1998]

I'm having trouble drawing a good geometry diagram.
 Drawing or Constructing an Ellipse or Oval [02/22/2006]

I know you can draw an ellipse using a string and two tacks. How do I
determine the length of the string and the location of the tacks to
draw an ellipse of a particular size?
 Find the Center of a Circle Using Compass and Straightedge [10/15/2003]

How can I find the center of a circle?
 Folding a Circle to Get an Ellipse [01/08/2001]

How can I prove that taking a point on a circle, folding it to an
interior point, and repeating this process creates an envelope of folds
that forms an ellipse?
 How Did Socrates Teach the Boy to Double the Area of a Square? [06/15/2010]

Reading Plato's Meno leaves a student confused about how the ancient Greeks scaled
squares. Doctor Rick walks through this story of Socrates and his method,
emphasizing that they would have approached this puzzle  as well as the
Pythagorean Theorem  geometrically.
 The Importance of Geometry Constructions [12/29/1998]

Why are geometry constructions important? What do we learn from them?
Where have they appeared in math history?
 Impossibility of Constructing a Regular NineSided Polygon [04/07/1998]

Can you construct a regular 9 sided polygon with just a compass and
straightedge?
 Impossible Constructions [01/14/1998]

What are the three ancient impossible construction problems of Euclidean
geometry?
 Impossible Constructions? [04/08/1997]

My geometry teacher told us there are 3 impossible problems or
constructions  what are they?
 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.
 Inscribing a Regular Pentagon within a Circle [04/15/1999]

What are the reasons for the steps in inscribing a regular pentagon
within a circle with only the help of a compass and a straightedge?
 Inscribing a Square in a Triangle [10/13/2000]

How do you inscribe a square in a scalene triangle?
 Line with Small Compass and Straightedge [10/16/1996]

Construct a line segment joining two points farther apart than either a
compass or the straightedge can span.
 NineSided Polygon [06/11/1997]

Can you construct a regular 9sided polygon inside a circle using only a
compass and straightedge?
 Octagon Construction Using Compass Only [02/22/2002]

Construct the vertices of a regular octagon using just a compass. The
only thing you know about the octagon is the circumradius.
 A Point in the Triangle [02/12/1999]

Finding the point P in a plane of triangle ABC, where PA + PB +PC is
minimum.
 Precision in Measurement: Perfect Protractor? [10/16/2001]

Given that protractors are expected to be accurate to the degree, and in
some instances the minute or second, how are angles accurately
constructed and marked?
 Proving Quadrilateral is a Parallelogram [11/30/2001]

We are having a problem with the idea of a quadrilateral having one pair
of opposite sides congruent and one pair of opposite angles congruent.
 Proving Quadrilateral Is a Parallelogram, Redux [04/04/2012]

A geometry teacher wonders if his student has proven that a quadrilateral with one
pair of congruent sides and one set of congruent angles is a parallelogram. By
following the steps from another Dr. Math conversation cited by the teacher, Doctor
Peterson illustrates the proof's hidden assumption with a counterexample.
 Regular Pentagon Construction Proof [11/23/2001]

What is the proof of the construction of a regular pentagon?
 Rotate the Square [09/19/2002]

Which points on the halfcircles are B and D?
 Sin 20 and Transcendental Numbers [6/29/1995]

What is the significance of sin 20 in geometry?
 Squaring the Circle [12/22/1997]

Can you construct a square at all with the same area as a circle with a
given radius?
 Squaring the Circle [3/16/1996]

Where did the phrase "squaring the circle" come from? We found it in
literature and wonder about its origins and what it means.
 Straightedge and Compass Constructions [12/14/1998]

Can you help me with these constructions, using only a straightedge and a
compass? A 30, 60, 90 triangle, the three medians of a scalene
triangle,...
 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.
 Triangle Construction [09/09/2001]

Given a triangle ABC and point D somewhere on the triangle (not a
midpoint or vertex), construct a line that bisects the area.
 Triangle Construction Given an Angle, the Inradius, and the Semiperimeter [03/26/2002]

Given an angle, alpha, the inradius (r), and the semiperimeter (s), construct the triangle.
 Triangle Construction Given Medians [12/12/2001]

Given median lengths 5, 6, and 7, construct a triangle.
 Trisecting a Line [11/03/1997]

How would you trisect a line using a compass and a straight edge?
 Trisecting a Line [01/25/1998]

Is it possible to trisect a line? (Using propositions 134, Book 1 of
Euclid's elements.)
 Trisecting a Line [01/30/1998]

How do I trisect a line using only a straightedge and compass?
 Trisecting a Line Segment [08/13/1999]

How can I measure onethird of a line of an unknown length using a
compass and a straightedge?
 Trisecting an Angle [11/21/1996]

Is there a proof that you can't trisect an angle?
 Trisecting an Angle [06/15/1999]

I've come up with a method of approximately trisecting any angle. Can you
tell me how accurate it is?
 Trisecting an Angle [06/17/2000]

I believe I have a simple straightedge and compass construction that
trisects any angle except a right angle, but have not been able to write
a proof...
 Trisecting an Angle [4/16/1996]

I can bisect an angle easily but I can't trisect it perfectly. Would you
please send me instructions?
 Trisecting an Angle: Proof [6/3/1996]

Is there a proof for how to trisect an angle?
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