The coalition government has announced that VAT will increase from 17.5% to 20% on January 4^th 2011.

Problem

A TV is advertised at £1000 including VAT at 17.5%.

VAT is increased to 20%.  What will the new price tag be?

Solution

The immediately apparent answer is £1025, because we’ve “added 2.5%”.  But that’s not quite right…

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[This problem is related to the (easier) 2-dimensional Diagonal Problem - click here for a full solution]

1. Imagine a cuboid made up of lots of little cubes.

2. Imagine a straight line (or “traversal”) connecting two opposite vertices of the cuboid

3. How many little cubes does the line pass through?

Note: Cubes are only counted if the traversal passes through them, so if your traversal goes exactly through a vertex or an edge separating cubes within the cuboid, then it is not considered to pass through the adjacent cubes.  In the 2×3×4 example shown, the traversal actually passes through an edge in the centre of the cuboid.

Problem: How many cubes does a traversal pass through in a 90×120×140 cuboid?

(Hint: Start small!)

Professor of Mathematics Marcus du Sautoy reveals the personalities behind the calculations and how mathematics is the driving force behind modern science and exploration.

Ten fascinating 15-minute radio programmes, all this week and next week on BBC Radio 4 at 3.45pm.

Catch up on BBC iPlayer (UK internet users only)

→Go to A Brief History of Mathematics site

1. Draw a rectangle on squared paper.
2. Draw a diagonal across your rectangle.
3. How many squares does it pass through?

Note: If your diagonal goes exactly through a point, like in the 2×4 example, then it is not considered to pass through either of the diagonally adjacent squares.

Problem: How many squares does a diagonal pass through in a 190×884 rectangle?b

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Problem:
When the area of the green square is two-fifths of the area of the whole diagram, what fraction do the four black triangles occupy?

Open the post to play with a Java applet.

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Happy Christmas from The Secret Garden of Maths!
http://news.bbc.co.uk/1/hi/uk/8428406.stm

Can you work out the size of angle xº?

That’s a regular hexagon and a regular pentagon.  Good luck!

(Hint: Consider the size of the interior angles in a polygon, the sum of angles round a point, and the sum of angles on a line)

(This is my first post in quite a while – apologies for the delay. I’ve been trying to become a qualified teacher!). [Read more →]

Want to lose weight fast?  Then jump on a plane to the equator!

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I was very saddened to hear today of Stephen Gateley’s sudden death.  Stephen gave a huge amount to pop music and was an inspirational figure.  May he rest in peace.

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