How did Dutch artist Leon Keer create a 3D illusion on a street in chalk? The same way they created perspective in Renaissance Florence

"Computers enable artists to calculate such effects with new precision – just as they enable 3D film-makers to achieve similar illusions. But all these modern wonders go back to the Renaissance when the closest thing to a computer was a set-square. The science improves. The locations change from churches and palaces to cinema screens and street surfaces. Our capacity for wonder lives on." (BBC) - http://bit.ly/zwfkuz

These are becoming more popular these days - it seems - but this video gives a little insight into the creation of an anamorphic street image.

http://www.youtube.com/watch?v=lm3bUEePRMU&feature=player_embedded

Spiralling into a trajectory?

"An Australian biology professor is causing a rumble in the academic jungle by suggesting that his country should import elephants and other foreign species into its wild interior.

"Take so many big species out of an ecosystem, and there are bound to be changes all the way down to its bottom.

"'We have a very unbalanced ecology and it's all just spiralling into a trajectory', lamented Prof Bowman."

I would love someone to provide a diagram or equation that would represent this 'spiralling into a trajectory'.

Read more at the BBC: http://bbc.in/wLStPv

Finding the truth and beauty in data

Typically short and superficial but this video clip shows some of the latest uses of technology for visualising data.

Link to BBC Technology page with video

Trains and planes mapped in 'real' time...nice.

Source - BBC News - © 2011 BBC

Language and Olympic ticket maths

http://news.bbc.co.uk/sport1/hi/olympics/13892584.stm

I cannot help but worry about the overall organisation of Olympics ticket sales when I read this:

A Locog statement read: "There has been unprecedented demand for cycling - every session and every price range was oversubscribed.

"Bradley and the team have made cycling one of the most popular sports at the London 2012 Games.

"We have developed an "athlete friends and family initiative" - a first - which enables all cyclists to buy two tickets to every event they compete in, so their friends and family can be there."

I don't quite see how having a 'pair' of tickets allows 'friends and family' to see Bradley Wiggins competing. A friend and a family member per event maybe but...

I still cannot persuade Locog to divulge the system used to allocate tickets in the initial ballot. A refusal of transparency smacks of something to hide to me.

Olympics tickets ballot

Does anyone know exactly how the ballot for tickets was operated - in detail?

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If the secretary of state says it's true, it's probably wrong

From the Guardian Diary:

guardian.co.uk, Tuesday 21 June 2011 22.45 BST

"Gove's law of education. If the secretary of state says it's true, it's probably wrong

"We are going to raise school standards. It is a given. Michael Gove is taking care of it. But he's a broad sweep man. Not so hot on the details, by all accounts. And we see that quite clearly in his quest to push the sciences. "What [students] need is a rooting in the basic scientific principles, Newton's laws of thermodynamics and Boyle's law," he told the Times. Which would have been a revelation to Newton himself. For he was responsible for the law of motion, not thermodynamics. Still, the day will come when everyone knows the difference and then all credit will go to Gove."

Oh dear, oh dear...

TI-84 • ATM

TI-84 review has just been posted to the website

Bad maths in the supermarket

Originally posted by nishwater on flickr with the following comment:

"At first glance you'd be forgiven for thinking that this is cheaper than the £23/kg parmesan sat next to it on the shelf "

What intrigues me is how the price per kilogram shown happened in the first place.

Fieldfares count Fibonacci

Two years ago it started with one fieldfare eating the apple windfalls outside my office.

It frequently had run-ins with a blackbird and so after a while it called in another fieldfare for support.

The blackbird was still hassling them however.

Next year a third fieldfare was called in and the blackbird responded by calling in some mates to help defend the winter food supply.

This year started with five fieldfares, and at the beginning of this recent cold snap there were a few more - three more in fact.

I am now looking out and can count exactly thirteen fieldfares engaged alternately in  feeding frenzy and bird wars with the increasing flock of blackbirds.

If I am not mistaken there should be 21 fieldfares tomorrow...

Has anyone got any spare windfalls?

To The Times, radius = diameter

Oh dear. Further (weak) coverage of the bicycle with Reuleaux polygon wheels.

The Times begins well by explaining the principles previously touched
on here but then goes on to expose it's correspondent's belief that
the radius is the same as the diameter. That is to say, since the
diameter of a Reuleaux polygon is constant then so must be the radius
but of course this not the case. The axle of a Reuleaux polygonal
wheel will rise and fall with it's forward progress.

Furthermore, if, as in this case, the front wheel is a Reuleaux
pentagon and the rear a Reuleuax triangle, the bobbing up and down
effect will be inconstant. Very uncomfortable if not nauseating.

http://technology.timesonline.co.uk/tol/news/tech_and_web/article6366308.ece

It's a Rouleaux Triangle/Pentagon etc

It has been pointed out to me that the answer to the question in my
last post is that we are talking about Reuleaux polygons. These are a
curve of constant width - that is, a curve such that, if two parallel
lines are drawn tangent to the curve, the distance between them does
not depend on their orientation.

Well, that's what Wikipedia says anyway:
http://en.wikipedia.org/wiki/Reuleaux_triangle

And this is confirmed by Wolfram Mathworld with a bit more technical
stuff: http://mathworld.wolfram.com/ReuleauxTriangle.html

I had forgotten about the rotary combustion engine which makes use of
the properties of such polygons:
http://auto.howstuffworks.com/rotary-engine2.htm

Thank you to Lyndon Baker for the original pointer to these resources.

What's do you call the shape of a UK 50p piece?

Can someone remind me what you call the sort of heptagon-type shape that is the UK 50p coin?

The reason I ask? I caught this news item at Ananova about Guan Baihua, 50, a retired military officer in Qingdao, who spent 18 months developing his unique bike.

"The front wheel is a five-sided pentagon while the back wheel is a triangle, reports the Bandao City Daily." says the news item and worse still, despite the obvious curved nature of the edges, Harshpaul at http://www.automotto.org/entry/man-gets-patent-for-odd-sided-wheels-bicycle/ says "A bicycle that has straight-edged wheels doesn't sound a very smart idea".

What I do know is that the curved sides are created as a section of a circle with its centre being the diametrically opposite corner. The effect being that the diameter of the shape remains the same, so to speak, thus allowing coins of this shape to roll through a coin-operated machine's internal workings just as easily as a circular coin. A cylinder (prism?) with such a cross-section will work perfectly as a roller. However, if the load is suspended on a central axle the effect can only be uncomfortable in a bike. All the more so with a five-sided front wheel and a three-sided rear wheel.

Anyway, the question was...what is the a curved-edged polygon thingy called?

Australian politician grows 2.7 metres taller

An Australian politician has had her legs lengthened according to
Ananova, an online news provider, . She is now over 4 metres tall
which should provide her with a dominating political presence in the
Logan city council chamber.

Fed up with what she saw as her diminutive height of 1.52m she paid a
Russian clinic to break her legs in four places and had them stretched
by "1mm a day for nine months". As a result, then, she is now 4.2
metres tall.

"Ms Ban was taunted at school and feared her height would damage her
credibility as she entered the legal profession and later went into
local politics." I reckon it's not her credibility that is damaged but
the basic mathematics of the journalist(s) involved.

You can read the full story here:
http://www.ananova.com/news/story/sm_3303713.html

I am so seriously under-weight...

According to a report in the UK Daily Mirror...

...I am so seriously under-weight that I am amazed I am still alive.

http://www.mirror.co.uk/life-style/dieting/2009/04/22/could-this-pill-really-be-the-diet-miracle-we-ve-been-waiting-for-115875-21295493/

In a report about this new diet medication the journalist tells us
that the pill is only available to those with a body mass index of 28
or more.

To check whether I qualified, I used their formula as published and my
Body Mass Index works out at 0.037.

Using the same algorithm I calculate that in order to qualify for the
pill I would either have to weigh 110g or be 49m tall.

Try the formula yourself:

BMI is a system used to determine how healthy your weight is in
relation to your height. Here's how to work out yours:

1 Measure your height in metres and multiply the figure by itself.

2 Measure your weight in kilos

3 Divide the weight by the answer to no.1

If you qualify for the diet pill with BMI of 28 or over using this
algorithm, then do let me know!

One dollar = one cent according to American phone company

Sometimes one can only despair...

You may remember a while back when a lottery company had to withdraw a scratchcard.

To qualify for a prize, users had to scratch away a window to reveal a temperature lower than the figure displayed on each card. As the game had a winter theme, the temperature was usually below freezing.

But the concept of comparing negative numbers proved too difficult for some Camelot received dozens of complaints on the first day from players who could not understand how, for example, -5 is higher than -6.

Well now I believe this has been trumped by Verizon, an American phone company...

Listen to a frustrated customer trying to get the customer service representatives to understand that when they quote 0.002 cents per kilobyte of data this does not mean that 35 000 kilobytes cost $70.

You just have to listen to the recorded conversation.

http://www.youtube.com/watch?gl=GB&v=lCJ3Oz5JVKs

Prime numbers and multiples of six...

There you are happily wandering through the pre-Christmas melee when, out of the blue, something of a revelation hits you right between the primes.

We, my nine year old twins and I, had spent the day chasing Christmas trees, writing cards, sorting out the lights and all those other festive bits and pieces. Lacking energy, I caved (well it didn't take much to be honest) and agreed to chips for tea. Added the compulsory greenery and we sat down to tea with the usual demand for a quiz (sometimes its our version of Twenty Questions...). Anyway Megan's chosen subject: Maths.

Mum invents the questions and to get to the point, a discussion ensued on how to identify whether or not a number is prime. Caitlin asks: "Is three billion and 1 a prime number?" I can't answer in the time available (Strictly Come Dancing is going to start soon). Then Caitlin announces that, apparently, all prime numbers are either one less than, or one more than a multiple of six. Therefore, it seems, that you can at least say that a number is not prime if that requirement is not met.

They all rushed off to watch the semi final - the maths of the SCD quarter and semi finals is another story - leaving me to discover that this multiple of six thing is true and to wonder why I had never heard that before. Maybe it's just me that it has passed by or that has passed it by...

Nine year olds...hah!

Why do car wheels have an odd number of spokes...

Sitting in a car park yesterday I was elevated in a moment of meditation to notice that the wheels on every# car I could see had an odd number of spokes.

Five spokes and seven seemed the most frequent but there was one with three spokes. There were none I could see with four, six or eight. Googling revealed this article which sort of discusses the axes of symmetry of a Ferrari wheel (five spokes) but only refers to the aesthetics rather than there being any engineering rationale behind the oddness.

A Google images search seems to indicate that odd is by far the overwhelming favourite for spokes but not exclusively so. It would seem that eight is not uncommon among what seem to be high-performance cars (those that are involved in high speed racing for example). Thus maybe it is just aesthetic. It would be interesting to hear what others think.

Event calendar now up and running

After a few trials and tribulations involving sending data from the calendar through Yahoo's website for processing and back to our Calendar web page the processing of event information now works. What was the problem? Well...in order to display the map of events it was necessary to extract the address information and encode that in a form for Google maps. Bizarrely, however, Google doesn't do that, but Yahoo does - through its data 'pipes' system. The data gets fed back to Google maps automatically allwing the bat indicators on the map to plot all the events that have sufficient information in them for Yahoo to pinpoint the location.

It's all very cunning and not a little mind boggling. But, hey, it works...

At the top of the page is a link to a form with which you can submit your event. It has to go past my eyes first however in order to avoid nonsense entries etc.