Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Use the applet to explore the area of a parallelogram and how it relates to vectors.
Use the applet to make some squares. What patterns do you notice in the coordinates?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
How well can you estimate angles? Playing this game could improve your skills.
Move the corner of the rectangle. Can you work out what the purple number represents?
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Under what circumstances can you rearrange a big square to make three smaller squares?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
Use these four dominoes to make a square that has the same number of dots on each side.
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
What happens when we add together two complex numbers?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
There are lots of ideas to explore in these sequences of ordered fractions.
What happens when we multiply a complex number by a real or an imaginary number?
It would be nice to have a strategy for disentangling any tangled ropes...
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Can you find triangles on a 9-point circle? Can you work out their angles?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
An environment that enables you to investigate tessellations of regular polygons
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?
Can you make sense of these three proofs of Pythagoras' Theorem?
Cartesian Coordinates are not the only way!
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
How good are you at estimating angles?
Join pentagons together edge to edge. Will they form a ring?
Let's go further and see what happens when we multiply two complex numbers together!
Can you devise a system for making sense of complex multiplication?
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?