Maths Item of the Month Archive

September 2010

Tom's Buttons

August 2010

Survival

Two people have been accused of being ‘in league with the devil’.

To test this they know they are going to be locked in separate sealed rooms where they cannot communicate with, or hear, each other.

Every minute for an hour they will each flip a coin and then make a prediction of the other person’s coin flip.

If on any one of the 60 predictions they are both right then this is sufficient evidence that they are ‘in league with the devil’ and they will both be killed.

There is a strategy they can use which will guarantee their survival.
What is it?

Solution

July 2010

Dissections

A square can be cut into six pieces that can then be arranged to form two different Greek crosses as shown below.




Can you cut the square into only five pieces that can then be arranged to form two different Greek crosses

Solution

June 2010

Different Distances

Arrange n counters in the cells of an nxn grid in such a way that distances between pairs of counters are all different. (Distances are measured in a straight line connecting the centres of the occupied cells.)
Solutions for n=3 and n=4 are shown below.


n=5,6,7 are also possible. Can your students find any of these arrangements?

Solution

Geogebra Demonstration (requires Java to view)

May 2010

Broken Reciprocal Key

The 1/x key on my calculator is broken. How can I use the trigonometry buttons to calculate reciprocals?

Solution

April 2010

MEI Mathematics Conference 2010

This year’s MEI Mathematics Conference will take place from July 1-3 at the University of Reading in Berkshire. It is designed to be a great occasion for everyone, whether your aim is to improve your teaching, to do some interesting mathematics, to engage with policy makers or to enjoy the company of other mathematicians.

Bookings are now being taken.

Programme and booking form

March 2010

Difference of two square roots

Is every positive integer power of the difference between the square roots of consecutive integers?

Solution

February 2010

Almost regular

Here is a technical drawing method for constructing a 'regular' polygon with n sides.

Draw an equilateral triangle ABC and a circle with diameter AB. Use the standard construction to find point D on AB such that BD: BA is 2:n. (The case n=5 is shown below)
Join C to D and extend this line to cut the circumference of the circle at E. BE is one side of the n-sided ‘regular’ polygon inscribed in the circle. The other sides can be swept out using compasses set at radius BE.

• Show that the method is not exact.


• Explain why it is a good approximation for small values of n.


• Investigate the method for large values of n.

Solution

January 2010

The medieval Italian painter Giotto is said to have sent the Pope a perfect circle that he had drawn freehand in evidence of his ability to do some decorative work. This became known as Giotto’s ‘O’.

“How would you judge a freehand circle drawing competition?”

Discuss! You can assume that, in judging the drawing competition, you have access to any measuring instruments. You can also assume that you are allowed to set any rules of the drawing competition.

This task was set for the poster round of 2008 national final of the Senior Team Mathematics Challenge organised by the Further Mathematics Network and the United Kingdom Mathematics Trust. Teams of four sixth form students were given one hour to produce a response to this question in the form of a poster. The content of the winning poster was used to produce this poster which was distributed to schools in England.

Download the winning poster (pdf)

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