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 TOPICS This page:   constructions    Search   Dr. Math See also the Dr. Math FAQ:   impossible   constructions Internet Library:   constructions HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Constructions Stars indicate particularly interesting answers or good places to begin browsing. Dividing a Line Segment into Seven Equal Parts [07/04/2003] I need to divide a segment with the length of X into seven equal parts using only a compass and straightedge. I also have to construct a line segment the length square root of X. 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 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 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, 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 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? Page: []

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