In 1975, a new word came into use, when a maverick mathematician made an important discovery. So what are fractals? And why are they important?

BBC News – article

Mandelbrot developed fractals as a mathematical way of understanding the infinite complexity of nature.

The concept has been used to measure coastlines, clouds and other natural phenomena and had far-reaching effects in physics, biology and astronomy.

Full Story – BBC News

You may have heard someone ask this question before.  You may have even pondered it yourself.

You need to get from A to B on foot, in pouring rain, without an umbrella (and without singing).
Presuming you want to get as little wet as possible, is it better to run or walk?

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By setting up a simplified mathematical model we can answer this question, and soon a solution will be made available.

In the meantime, we want your ideas!

If you want to submit a well-presented mathematical solution, it will be considered to be formally added to the post.

But of course, all comments are welcome, so please leave your suggestions below.

Physicists have explained one of football’s most spectacular goals.

More importantly, the mathematics of infinity features in a BBC News report!

Full story: BBC News website Read more…

There are plenty more where this one came from.  Although this is the only one that swears.  The others dance, and when I’ve done a bit more research on the Parametric B-Function (discovered through serendipity) I shall blog the findings.

This is made from a quintic graph (a polynomial of degree 5).  It’s possible to apply the Parametric B-Function to any y=f(x) graph, including reciprocal, hyperbolic and trigonometric functions.  I’m determined to find a practical use for the function.  I’m thinking music.  Watch this space. Read more…

The coalition 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…

Read more…

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

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 60×120×156 cuboid?  (Hint: Start small!)

Read more…

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.

→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

Read more…

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.

Read more…

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