Plus Blog

June 21, 2011

The strawberries are out and it's raining... so it must be Wimbledon time! If you're trying to while away the time waiting for the covers to come off the court then give Cliff Richard a break and take a look at some of the great tennis articles and puzzles here on Plus!

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Anyone for tennis (and tennis and tennis...)?
American John Isner and the Frenchman Nicolas Mahut are set for a rematch in the Wimbledon 2011 Championships — but how will it compare with their match of epic proportions from last year? Just how freaky was their titanic fifth set from 2010 and what odds might a bookmaker offer for a repeat?

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Making a racket: the science of tennis
A perfect althletic performance takes more than training, it also takes engineers working hard to produce the cutting-edge equipment. If you're a tennis player, your most important piece of equipment is your racket. Over recent decades new materials have made tennis rackets ever bigger, lighter and more powerful. So what kind of science goes into designing new rackets?

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Winning at Wimbledon
What does it take to win at Wimbledon? Can you figure out how many games the champion has to win? And how many matches are played overall?

And you can also find out if the robots have their eye on the trophy, if tennis should be in the Olympics and much, much more about maths and sport on Plus and on the MMP's Countdown to the Games.

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June 7, 2011

How big is the Universe? And how small is the smallest thing within it? This cute website developed by Cary Huang puts things into perspective. It lets you explore the entire range of scales, from the smallest length (the Planck length) all the way up to the entire Universe, via atoms, people, giant earthworms, planets, galaxies and more.

http://www.primaxstudio.com/stuff/scale_of_universe/

 

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June 7, 2011

Kneeling in the mud by a country road on a cold drizzly day, I finally appreciated the wonder that is a lever. I was trying to change a flat tyre and even jumping on the end of the wheel wrench wouldn't budge the wheel nuts. But when the AA arrived they undid them with ease, thanks to a wheel wrench that was three times the size of mine. There you have it ... size really does matter!

lever

Image by CR

A lever is a truly remarkable device that can literally give any of us the strength of ten men. You can counteract 10 men pushing down on one side of a see-saw by applying just 1/10th of their force, as long as you are 10 times further from the see-saw's centre as they are.

This is because the forces acting on a lever are proportional to the distances they are from the fulcrum. In this way a small amount of force moving a longer distance can move a large load over a smaller distance.

Levers are working hard all around us: in see-saws (where the fulcrum is between the loads), in wheel barrows (where the load is between the fulcrum and the force) and even in our very jaws (where the force is applied between the fulcrum and the load).

Archimedes was the first to mathematically describe how levers work and famously said: "Give me a place to stand, and I shall move the earth with a lever." And give me a long enough wheel wrench and I might just be able to change my next flat tyre for myself!

You can read more about levers from Wikipedia, and more about mechanics and about Archimedes on Plus

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May 26, 2011
<i>Pegasus</i> made by Robert J. Lang from one uncut square of Korean hanji paper. Image courtesy <a href='http://www.langorigami.com'> Robert J. Lang</a>.

Pegasus made by Robert J. Lang from one uncut square of Korean hanji paper. Size: 7 inches. Image courtesy Robert J. Lang.

If you've ever marvelled at the elegance of a paper crane or just struggled to refold a map you will enjoy the next Maths-Art seminar from the London Knowledge Lab.

Applications of Origami will be a practical, hands-on workshop and presentation by Mark Bolitho and members of the British Origami Society. The presentation will cover recent developments in origami and present some of the projects Mark has worked on. It will also review how origami techniques have been adopted in applied design from architecture to product design.

DATE: Thursday 9th June
TIME: 5.00 to 7.30pm
PLACE: London Knowledge Lab, 23-29 Emerald St, London, WC1N 3QS

The Maths-Art seminars are free to attend and everyone welcome. You don't need a reservation but an email to lkl.maths.art@gmail.com is appreciated for planning purposes. You can also watch past Maths-Art seminars on YouTube and read more about the maths of origami on Plus.

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May 11, 2011
Triangulation of surface

Ah the humble triangle. This simple shape is one of the first we ever learn. But perhaps you didn't realise just how important triangles are...

A triangle is a three-sided polygon and comes in a variety of flavours. Some are to do with the length of the triangle's sides: equilateral — where all the sides (and all the angles) are the same size; isosceles — where two of the sides (and two of the angles) are the same size; and scalene — where none of the sides (or angles) are the same. The angles inside the triangle are also important. All the angles add to 180°. You can have acute triangles, where all the angles are less than 90° and obtuse triangles, where one of the angles is greater than 90°. And of course you can get right-angled triangles — one of the most important mathematical shapes inspiring Pythagoras' Theorem and trigonometry.

But triangles aren't just mathematically significant, they are also fundamental to the way we build in our environments, both physical and virtual. Triangles are special because they are exceptionally strong. Out of all the two-dimensional shapes we can make out of straight struts of metal, only a triangle is rigid. All other shapes can be deformed with a simple push if the shape is hinged at the corners (eg. a rectangle could be pushed over into a parallelogram). But not the trusty triangle, which explains its ubiquitous use in construction from pylons to bracing.

Triangles are also special because they are the simplest polygon — it is a common approach to a tricky geometrical problem, such as analysing a complex surface, to instead approximate it by a mesh of triangles. This approach is also used in the real world to achieve some of the exotic shapes we now see in modern architecture, such as the curved shape of 30 St Mary's Axe, aka the Gherkin, or the canopy over the courtyard in the British Museum.

This method of triangulation also is vital in building our virtual world. The fluid forms of the CGI characters we see in film and on TV are actually an incredibly fine mesh of triangles, in order that they can be stored and manipulated digitally.

Triangles — the simplest shape that makes our mathematical, physical and digital worlds go round.

You can read more about triangle strength and their role in our physical and virtual worlds on Plus. And you can find out all about their role in mathematics at Wolfram MathWorld.

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May 11, 2011

We came across the excellent Math Encounters Blog through their post Dimensional Analysis and Olympic Rowing, a response to the New Scientist article by Plus author, John Barrow.

Math Encounters is about those problems we might encounter any day where a little bit of maths can really help. Posts cover the maths of carpentry, drinking, management and much more. The maths can be quite surprising and is always clearly explained. And unlike many other popular science and mathematics blogs, it definitely doesn't shy away from the interesting details!

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