# As Pythagoras said just the other day...

The corridor down to the maths room at Southgate School, north London, is lined with pictures, including copies of Josef Albers' "Homage to the Square" and artist Bridget Riley's optical images, bending black and white lines and teasing the retina. Enter the room and a PowerPoint presentation featuring Pythagoras is playing.

Out of the sculpted head of the noble Greek spout speech bubbles: "Hi, I'm Pythagoras. I was born about 569bc on the Greek island of Samos, just off the coast of what is now western Turkey. I died some 90 years later...

nearly 2,500 years ago. I travelled far and wide... visiting Egypt and old Babylon and, some say, even India... The Buddha was preaching and Confucius was alive and well in China." A map shows his journeys around the Mediterranean as arrows dash around the screen. The presentation goes on as the students enter and settle.

"Raphael Sanzio painted me and my mates for Pope Julius II in the early 1500s on a wall in the Vatican in Rome. You can still see meI down there on the leftI with a beard and no hair!" The screen lights up with the picture from the Vatican with arrows racing in to indicate the great thinkers featured: Diogenes, Socrates, Plato.

Pythagoras goes on to explain: "I was a philosopher, a diplomat, a musician, a prisonerI and, some say, even a murderer. But above all I was a mathematikoi in the secret society I founded at Croton in what is now south Italy." He describes his lifestyle, believing in vegetarianism and the equality of the sexes.

The sequence ends with Pythagoras admitting that what we call Pythagoras's theorem was already known: "the ancient BabyloniansI the ChineseI the EgyptiansI and the mathematicians of India all knew that 'the square on the hypotenuse is equal to the sum of the squares on the opposite two sides'. I wasn't even born when they were using Pythagoras's theorem."

The students go on to discover that the unfortunate mathematician died a violent death in his commune when it was attacked.

They hardly have time to digest all of this when up on the screen comes a series of questions. Your starter for 10...

What is the square root of 121? What is 101 minus 91?

Excel generates the questions randomly: random numbers and random questions. "The starters are easy to put up on the screen. It gets them thinking right from the word go," says maths teacher David Whitfield.

"Every time you run something like this the questions are different. It is a front-loaded investment. There is a certain amount of work, a couple of hours initially, but after that you could use them for eternity and it will always bring up different questions.

"You do need lots and lots of questions and I find it quite hard to generate them. The computer doesn't. You can come up with the criteria that you want to test and the level of complexity, and once you have decided that and put it into the computer it will just keep coming up with questions. You can use Excel to either to hide or show the answers."

After this, David Whitfield uses his laptop and the software Geometer's Sketchpad to show how Pythagoras works. He puts squares on to each side of the triangle and changes the size of the triangle. All the pupils can see that no matter what you do to the right-angled triangle, the theorem remains true. He says: "That ratio just stays fixed no matter what you do with the triangle. You can demonstrate a visual proof."

For another view, back to PowerPoint and Pythagoras. "Hi!" says the on-screen Pythagoras. "This is the theorem named after me." Sliding across the screen is a yellow right-angled triangle, c2 = a2 + b2. Back comes Pythagoras. "Let's look at it this way," he says, and the yellow triangle returns on-screen to be joined by a red square that attaches itself to the hypotenuse. Soon a green square and then a blue square attach themselves to the other two sides. The red square moves, as do the other two to demonstrate the truth of the theorem. Everyone looks convinced.

Homework is set around the theorem and the pupils are referred to David Whitfield's website where they can get both assistance and inspiration.

He is never afraid to experiment. Recently in teaching maths he has explored the crimes of Al Capone, as well as looking at the mathematicians and code breakers of Baghdad, he has also explored the intricate geometry of the anonymous weavers of carpets in the Middle East.

Take a trip to his website to find out, and as David Whitfield himself writes on the site: "The greatest mathematicians could also be members of secret cults, alchemists, obsessive gamblers, neurotics, gentlemen scribblers, feminists and revolutionaries, US presidents, crowd-stirring orators, poverty-stricken aesthetes or lowly railway clerksI and sometimes just shy and unassuming people who lived in the semi-detached at the end of the cul-de-sac."

David Whitfield was runner-up for the New to Teaching section (sponsored by The TES) of the Becta ICT in Practice Awards 2004.

RESOURCES

Hardware

Laptop computer, projector, screen.

Software

PowerPoint; Excel

www.microsoft.comoffice

Geometer's Sketchpad

www.keypress.comsketchpad

Autograph

www.autograph-math.com

Resources developed by David Whitfield can be downloaded from the teacher resources pages at:

www.pifactory.co.uk and www.lgfl.netlgflleasenfieldschoolssouthgateaccountsstaffdwhitfieldw ebpagesteacher_resources_contents.html

Useful websites

Biographies pages of the MacTutor history of mathematics archive: http:turnbull.mcs.st-and.ac.ukhistoryBiogIndex.html

Ron Knott's site for everything on the wonders of numbers: www.ronknott.com

Eric Weisstein's Mathworld site: http:mathworld.wolfram.com

Plus magazine (part of the Millennium Maths Project)

http:plus.maths.orgindex.html

Nrich (from the Millennium Maths Project): http:nrich.maths.orgpublicindex.php

Centre for innovation in maths teaching, Exeter University: www.ex.ac.ukcimt

Megamath from Los Alamos: www.c3.lanl.govmega-math

Cut the knot (interactive maths): www.cut-the-knot.orgfront.shtml

Math dot com (reference materials, games and "ask an expert"): www.math.comindex.aspx

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