Resources tagged with: Constructions
There are 31 NRICH Mathematical resources connected to Constructions, you may find related items under Transformations and constructions.
Broad Topics > Transformations and constructions > Constructions
The Farmers' Field Boundary
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
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?
Constructing Triangles
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
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...
Curvy Areas
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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.
Triangle Midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Cool as Ice
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Flip Your Mat!
What shape and size of drinks mat is best for flipping and catching?
A Rational Search
Investigate constructible images which contain rational areas.
Moving Squares
How can you represent the curvature of a cylinder on a flat piece of paper?
Close to Triangular
Drawing a triangle is not always as easy as you might think!
Folding Fractions
What fractions can you divide the diagonal of a square into by simple folding?
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?
Jomista Mat
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Mathematical Patchwork
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
A Patchwork Piece
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Half a Triangle
Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
Yin Yang
Can you reproduce the Yin Yang symbol using a pair of compasses?
Pentabuild
Explain how to construct a regular pentagon accurately using a straight edge and compass.
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.
Golden Construction
Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
Circle Scaling
Describe how to construct three circles which have areas in the ratio 1:2:3.
LOGO Challenge 8 - Rhombi
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
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.
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?
The Medieval Octagon
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Pareq Exists
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Gold Again
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
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?