Regular polygons and circles
-
-
problemFavouriteRound and Round the Circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
-
problemFavouriteEgyptian Rope
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
-
problemFavouriteShapes on the Playground
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
-
problemFavouriteOverlapping Again
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
-
interactivityFavouriteTessellation Interactivity
An environment that enables you to investigate tessellations of regular polygons -
problemFavouriteRolling Around
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?
-
problemFavouriteSalinon
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
-
problemFavouriteCurvy Areas
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
-
problemFavouriteSemi-Detached
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.