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Resources tagged with Straight edge & compass constructions similar to Weekly Problem 33 - 2007:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > 2D Geometry, Shape and Space > Straight edge & compass constructions

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Two Points Plus One Line

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line,. . . .

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Circle Scaling

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.

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Squirty

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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The Medieval Octagon

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

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Pentagon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the vertices of a pentagon given the midpoints of its sides.

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Triangle Mid Points

Stage: 4 Challenge Level: Challenge Level:1

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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A Rational Search

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate constructible images which contain rational areas.

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Folding Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Close to Triangular

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Drawing a triangle is not always as easy as you might think!

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Golden Trail 1

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

A first trail through the mysterious world of the Golden Section.

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Half a Triangle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

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Pareq Exists

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

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Cool as Ice

Stage: 3 and 4 Challenge Level: Challenge Level:1

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

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Flip Your Mat!

Stage: 2 and 3 Challenge Level: Challenge Level:1

What shape and size of drinks mat is best for flipping and catching?

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Moving Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How can you represent the curvature of a cylinder on a flat piece of paper?

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Mathematical Patchwork

Stage: 2 and 3

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.