Categories

A ladder seen from the side is sliding down a wall. Prove that a fixed point on the ladder traces part of an ellipse.

Categories

## The flat earth

An observer is standing on a plane at h metres below the centre of a reflecting sphere of radius r. Another object on the plane is perceived at an angle α from the vertical. What is α of the horizon in terms of h and r?

Categories

## Camera obscura

A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?

Categories

## Pulling the strings

Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.

Categories

## The arena

In a circular arena two contestants are leaving from points A and B. Their respective speeds are such that they would collide at point C, but just before they do they exchange directions. Then they hit the edge of the arena and return to their starting points. During the whole race, A and B move at constant but not necessarily equal speeds. Which contestant returns to his starting point first?

Categories

## The rolling stones

If you roll a circle down a parabola, small circles can roll all the way down and up, whereas large circles get stuck between the sides at some point. What is the transition radius? In other words, what’s the maximum circle that keeps on rolling?

Categories

## The magic mirror

You are standing in front of a mirror. Your shoulder width is 50 cm and your eyes are 6 cm apart. What is the minimum mirror width for a stereo view of yourself?

Categories

## The ricochet

An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?

Categories

## Triangular billiards

A ball track starts halfway the left side of an equilateral triangular billiard table having side length 2. After two bounces it arrives in the top corner. What’s the total track length?

Categories

## The pulley problem

Two pulleys carrying three weights of 30, 70 and 50 grams. Given that the constellation is in equilibrium, what’s the angle?