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Five Circuits, Seven Spins
A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
Approximating Pi
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
A Rolling Disc - Periodic Motion
Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?
Age 16 to 18 Challenge Level:
 |
A length of thin wire ($L$ ) binds together two
cylindrical welding rods, whose radii are $R$ and $r$ , by passing all
the way around them both.
Find $L$ in terms of $R$ and $r$. |
Circumference and arc length. Circle properties and circle theorems. Sine rule & cosine rule. Similarity and congruence. Regular polygons and circles. Pythagoras' theorem. Trigonometric identities. 2D shapes and their properties. Sine, cosine, tangent. Creating and manipulating expressions and formulae.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.