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There are **31** NRICH Mathematical resources connected to **Constructions**, you may find related items under Transformations and constructions.

Problem
Primary curriculum
Secondary curriculum
### The Farmers' Field Boundary

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Square Under the Hypotenuse

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Constructing Triangles

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Rotations

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curvy Areas

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squirty

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Midpoints

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cool as Ice

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

Age 11 to 16

Challenge Level

Project
Primary curriculum
Secondary curriculum
### Flip Your Mat!

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Rational Search

Investigate constructible images which contain rational areas.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Moving Squares

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Close to Triangular

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Folding Fractions

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

Age 14 to 16

Challenge Level

General
Primary curriculum
Secondary curriculum
### 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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Jomista Mat

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

Age 7 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Mathematical Patchwork

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

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### A Patchwork Piece

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Half a Triangle

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Yin Yang

Can you reproduce the Yin Yang symbol using a pair of compasses?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pentabuild

Explain how to construct a regular pentagon accurately using a straight edge and compass.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Points Plus One Line

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, which is equidistant from A and B.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Construction

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Circle Scaling

Describe how to construct three circles which have areas in the ratio 1:2:3.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 8 - Rhombi

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

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 2 - Diamonds Are Forever

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.

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Folding Squares

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Medieval Octagon

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pareq Exists

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gold Again

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Kissing

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?

Age 16 to 18

Challenge Level