Author Archive

## GeoGebra: Binomial Distribution with Normal and Poisson Approximation

##### Click the image to link to GeoGebraTube (Opens in a new window/tab). .

This applet is for visualising the Binomial Distribution, with control over n and p.

It also shows the Normal Approximation curve (and how this approximation breaks down for large or small p)
and it shows the Poisson Approximation curve (and how his approximation breaks down if there’s no positive skew)

You can show critical regions at either end by turning the bars red instead of green. The appropriate cumulative binomial probabilities are shown.

## Pythagoras’ Theorem works with Negative Length

March 31st, 2011 1 comment

When taking square roots of both sides of an equation, one should be careful not to turf out the negative result without first considering whether it has a true meaning.  When using Pythagoras’ Theorem, the last step is to take square roots. So, can we have a hypotenuse with length -5?

## Using the mean to find the mode of a Binomial Distribution

The original motivation behind this investigation was an attempt to save my Statistics students a few precious seconds in their upcoming S1 module paper.

The mean or expectation of a Binomial Distribution is always very close to mode, (the value of X that has greatest probability). I want to know if you can use the mean to reliably predict the mode.

## Money, Debt & Greed – A Brief Commentary

March 9th, 2011 1 comment

### On Friday I will be talking in our school chapel. Here is the penultimate draft of the monologue (the style does lend itself to being read out loud)

Good morning.

I want to talk to you today about our monetary system.  Most, perhaps all, of us here at Forest School have benefited from the monetary system.  Money affords us food, entertainment, transport, holidays; a place to live; stability.  Money creates incentives; it gives us jobs, careers and aspirations; and taxes allow huge investments like high-speed rail links and the Olympic park.

But does everyone benefit from our monetary system?

We’re born into a society of which money seems to be the driving force.  Where does money come from? Who gives us it to spend?

## Ballcam

March 9th, 2011 1 comment

Please forgive my appalling lack of posts in recent months.  I’ve been working on a project with the above name, which seeks to place cameras in objects that can rotate on any axis, a football for example!  Exciting stuff, but I can’t share the maths with you on here.

## Mathart

November 29th, 2010 1 comment

## How Mandelbrot’s fractals changed the world

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

## ‘Fractal’ mathematician Benoit Mandelbrot dies aged 85

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

## I’m Singin’ in the Rain…

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?

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.

## Roberto Carlos wonder goal ‘no fluke’, say physicists

September 3rd, 2010 1 comment

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…

## The Swearing Graph!

September 2nd, 2010 1 comment

This is made from a quintic graph (a polynomial of degree 5).  It’s possible to apply the “treatment” to any function, including reciprocal, hyperbolic and trigonometric functions. Read more…