Other tags that relate to Polycircles
Creating and manipulating expressions and formulae. Generalising. Simultaneous equations. GeoGebra. Making and proving conjectures. Interactivities. Visualising. Dynamic geometry. Regular polygons and circles. 2D shapes and their properties.There are 90 results
Broad Topics > Physical and Digital Manipulatives > GeoGebra
The Medieval Octagon
Age 14 to 16
Challenge Level
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Arrowhead
Age 14 to 16
Challenge Level
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?
Quad in Quad
Age 14 to 16
Challenge Level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Tilting Triangles
Age 14 to 16
Challenge Level
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?
Rolling Around
Age 11 to 14
Challenge Level
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?
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Cyclic Quadrilaterals
Age 11 to 16
Challenge Level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Squaring the Circle and Circling the Square
Age 14 to 16
Challenge Level
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Tessellation Interactivity
Age 7 to 16
Challenge Level
An environment that enables you to investigate tessellations of regular polygons
Bow Tie
Age 11 to 14
Challenge Level
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.
Using Geogebra
Age 11 to 18
Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.
More Magic Potting Sheds
Age 11 to 14
Challenge Level
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?
L-triominoes
Age 14 to 16
Challenge Level
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Picturing Triangular Numbers
Age 11 to 14
Challenge Level
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Angles Inside
Age 11 to 14
Challenge Level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
Overlap
Age 11 to 14
Challenge Level
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. . . .
Mixing Paints
Age 11 to 14
Challenge Level
Can you work out how to produce different shades of pink paint?
Mixing More Paints
Age 14 to 16
Challenge Level
Can you find an efficent way to mix paints in any ratio?
Farey Sequences
Age 11 to 14
Challenge Level
There are lots of ideas to explore in these sequences of ordered fractions.
Speeding Up, Slowing Down
Age 11 to 14
Challenge Level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
Shear Magic
Age 11 to 14
Challenge Level
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
More Twisting and Turning
Age 11 to 16
Challenge Level
It would be nice to have a strategy for disentangling any tangled ropes...
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
A Tilted Square
Age 14 to 16
Challenge Level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Where Is the Dot?
Age 14 to 16
Challenge Level
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Right Angles
Age 11 to 14
Challenge Level
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Subtended Angles
Age 11 to 14
Challenge Level
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?
Triangles in Circles
Age 11 to 14
Challenge Level
Can you find triangles on a 9-point circle? Can you work out their angles?
Square Coordinates
Age 11 to 14
Challenge Level
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?
Pegboard Quads
Age 14 to 16
Challenge Level
Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?
Guesswork
Age 14 to 16
Challenge Level
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.
Just Rolling Round
Age 14 to 16
Challenge Level
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?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Partitioning Revisited
Age 11 to 14
Challenge Level
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
Strolling Along
Age 14 to 18
Challenge Level
What happens when we multiply a complex number by a real or an imaginary number?
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
A Brief Introduction to the Argand Diagram
Age 14 to 18
Challenge Level
Complex numbers can be represented graphically using an Argand diagram. This problem explains more...
Is There a Theorem?
Age 11 to 14
Challenge Level
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?
Into the Wilderness
Age 14 to 18
Challenge Level
Let's go further and see what happens when we multiply two complex numbers together!
Mapping the Territory
Age 14 to 18
Challenge Level
Can you devise a system for making sense of complex multiplication?
Same Length
Age 11 to 16
Challenge Level
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Surprising Equalities
Age 14 to 18
Challenge Level
Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?
Mediant Madness
Age 14 to 16
Challenge Level
Kyle and his teacher disagree about his test score - who is right?
4 Dom
Age 5 to 16
Challenge Level
Use these four dominoes to make a square that has the same number of dots on each side.
Solving Together - Estimating Angles
Age 11 to 14
Week 2
How well can you estimate angles? Playing this game could improve your skills.
Points in Pairs
Age 14 to 16
Challenge Level
Move the point P to see how P' moves. Then use your insights to calculate a missing length.
Parallel Lines
Age 11 to 14
Challenge Level
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
NRICH is part of the family of activities in the Millennium Mathematics Project.