Mathematics

Picking Balls

A bag contains four balls – two red, one white and one blue. Someone takes two balls from the bag and tells you that at least one of them is red. What is the probability that the other is red? This is a simple logic problem which seemed to cause quite a few problems – […]

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Quadratic Equations

This is for Thomas and Emma and all those who loved mathematics at school. We want to solve a quadratic equation which can be written in the form you can try to guess the roots but is very rarely easy outside of school text books. However we can solve it by a method called ‘completing […]

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Converting Radians in Degrees Latitude and Longitude

The task of converting radians to degrees is reasonably trivial. However, latitudes and longitudes are usually expressed in the range -90 to 90 for longitude and -180 to 180 for latitudes. This is only a convention – latitudes above 90 have real unique meaning and they should not create any problems in google maps etc. […]

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More On Probability – At Least One Six in Six Throws of a Die

It is easy to work out how likely it is that you will throw six sixes in six throws of a die. there is 1/6 probability that you will throw a six therefore there is a  (1/6)6 probability that you will throw 6 in a row. However, if we want to know the probability that […]

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Paper Sizes

Paper Sizes Here is a list of paper sizes – see further down for how this is calculated. Paper Size Width (mm) Heigh (mm) A0 840.9 1189.2 A1 594.6 840.9 A2 420.4 594.6 A3 297.3 420.4 A4 210.2 297.3 A5 148.7 210.2 A6 105.1 148.7 A7 74.3 105.1 A8 52.6 74.3 Zoom Here are the […]

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Secular and Transient Equilibrium Formula

I will give the full derivation since although it is quite long and looks complicated it uses nothing more than A-level mathematics. Despite this the solution of the differential equations is usually given as a standard solution rather than derived. Consider a parent isotope (P) decaying into a daughter product (D). The rate of decay […]

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Probability and Significance

We often see things that say “No Link Between Cancer and Nuclear Plants” or nuclear power is safe. One of the reasons for this is the failure to understand the results of various studies or even gross misrepresentation of the results. This is just a basic information about probability and the statistical significance of some […]

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Exponents, Powers of Ten and Logs

You may have come here just to find out about unit prefixes – Mega, Giga, milli etc. However, it is a good idea to understand how to multiply and divide exponents as well so the first bit is worth reading. Notation In physics we often come across quantities that are multiplied by itself. For example […]

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