IN HONOUR OF Maths Week, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

Jack and Jill

The Ancient Greeks made enormous strides in the development of geometry.

The Greek mathematician Euclid works forms the basis for much of traditional geometry, relying on axioms and postulates to develop theorems that described properties and relationships of lines and shapes. Euclid’s Elements was the standard work on geometry for over two thousand years.

Lesser known is Hero of Alexandria who lived in the 1st Century CE and was a mathematician and engineer. While he did give us a useful formula for the area of a triangle, he also came up with a beautifully solution to what is now known as Hero’s problem, which we will pose as follows.

Jack and Jill live in houses some distance apart on the same side of a very straight river. Jack must visit Jill but on the way fetch a pail of water from the river.

Jack, very reasonably, wants to know how to find the shortest total journey.

Hero found a method without complex mathematical techniques. Can you?

Eoin Gill Eoin Gill

Friday’s puzzles: The answers

1. Area of red square = 64 square metres
2. A rectangle 10m x 4m with a 0.5m path around it is actually a rectangle 11m x 5m = 55 square metres.
3. b) One 16-inch pizza has an area of 201 square inches, while one 10-inch pizza has an area of 78 inches. Two 10-inch pizzas therefore would only give you 157 square inches.

Come back tomorrow for the answers to today’s puzzle. 

The puzzles this week have been compiled for The Journal by Eoin Gill of Maths Week Ireland and South-East Technological University (SETU).