##### Click the image to link to GeoGebraTube

(Opens in a new window/tab).

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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.

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?

Read more…

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.

Read more…

### 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?

** Read more…**

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.

November 29th, 2010
Micky
Tonight I made these instead of tidying my flat

**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

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

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?

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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.

But of course, **all comments are welcome**, so please leave your suggestions below.

September 3rd, 2010
Micky
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…

September 2nd, 2010
Micky
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…