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Browse High School Constructions

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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 Nine-Sided 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.

Nine-Sided Polygon [06/11/1997]
Can you construct a regular 9-sided polygon inside a circle using only a compass and straight-edge?

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 angles 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 counter-example.

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 half-circles 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, onstruct 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 semi-perimeter (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 1-34, 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 one-third 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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