Constructions

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Mathematical patchwork

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
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Making maths: stars

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?
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LOGO challenge 2 - diamonds are forever

Age

7 to 16

Challenge level

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
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LOGO challenge 8 - rhombi

Age

7 to 16

Challenge level

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
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Golden construction

Age

16 to 18

Challenge level

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
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Three tears

Age

14 to 16

Challenge level

Construct this design using only compasses
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Jomista mat

Age

7 to 11

Challenge level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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Kissing

Age

16 to 18

Challenge level

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
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Gold again

Age

16 to 18

Challenge level

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
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Pareq exists

Age

14 to 16

Challenge level

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