The Maths Thread

When I did my degree I really enjoyed some of the investigative ‘puzzles’ where you had to learn something each time you wanted to take the next step. When I became a teacher these investigations were part of the exam process at GCSE, not sure if they are now, and really sorted out how much you knew. Mind you they were open to abuse by unscrupulous teachers who wanted results. I used to mark my students papers with comments if they had been given a nudge to the next level but I know many who wouldn’t say anything.

Still ‘twas my favourite when studying.
 
One of the nicest puzzles I came across was this:

Imagine a circular lawn radius R. At the perimeter of the lawn, stands a goat, tethered to a stake planted at the edge of the lawn. The goat is tethered by a rope, length L. How long does the rope have to be, such that the goat can eat only half the grass?

(And of course the puzzle assumes the goat is small is relation to the size of the lawn and other such simplifications.)

It's such a simple, but fiendishly difficult little mathematically challenge. Good luck if you fancy a go at it.
 
One of the nicest puzzles I came across was this:

Imagine a circular lawn radius R. At the perimeter of the lawn, stands a goat, tethered to a stake planted at the edge of the lawn. The goat is tethered by a rope, length L. How long does the rope have to be, such that the goat can eat only half the grass?

(And of course the puzzle assumes the goat is small is relation to the size of the lawn and other such simplifications.)

It's such a simple, but fiendishly difficult little mathematically challenge. Good luck if you fancy a go at it.

is it... the square root of (pi x R)^2/2

this could be absolutely miles off...
 

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