Arithmo-geometric series A straightforward one page derivation of a formula not given on the internet that I can find.
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cubics.pdf How to determine the coefficients of a cubic equation from the sequence of numbers
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falling factorials An investigation into falling factorials - there is precious little on the internet about this.
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distance point to line An investigation using TI83/84 and a proof of the formula by induction - a proof that is not incomprehensible.
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fibonnacci_1 An initial investigation into Fibonnacci numbers with an explanation of the key properties and their link to Pascal's triangle.
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Easter How to calculate Easter from first principles.
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forward difference tables An initial investigation on how to deduce the function from any algebraic sequence of numbers.
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golden ratio An investigation into the relationship between the golden ratio and sin 72º
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kaprekar numbers A great idea from an Indian Mathematician with a passion for numbers.
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linear equation with ti-83 A neat way to produce a linear function from two points using linear regression.
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hexagon flowers An article I had published in a school's mathematical journal before I knew more about algebriac sequences.
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linear equations A back-to-basics introduction to linear equations and how to derive them from gradients and coordinates.
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partitions The results of an initial investigation into partitions giving an insight as to how the patterns arise.
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multigrades That multigrades even exist is a mystery but here's the reason using some tedious algebra.
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pentatope numbers Pentatope numbers are the number of intersections of vertices of an irreular n-gon and appear in Pascal's triangle.
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perfect amicable numbers What are they and how to find some of them. Can we ever find all of them?
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periodicity trig functions An investigation into the periodicity of sin and sinh and the relationship between the two.
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planck units A summary calculation of the Planck units from the constants of nature and deducing how many universes you can fit inside a hydrogen atom.
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polygon formula A simple investigation deriving the all the polygonal numbers
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road_capacity An explanation why queues form on motorways that disappear as myseriously as they appear. The answer is counter intuitive.
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shortest path How does a photon know before it sets off the quickest way to get from A to B? That's the mystery but here's the mathematics.
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triangular numbers A quick investigation into the connection between triangular numbers and combinations.
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toilet roll length Having calculated the length of a toilet roll the hard way I then realised how to do it in one line..
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trapezoidal numbers What are trapezoidal numbers and should teachers set impossible homeworks to find something that doesn't exist?
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volume frustrum The mathematical derivation of the volume of a frustrum and the intuitive way that actually takes longer.
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power sums This investigation led to the discovery of perfect digital invariants PDIs and recurring digital invariants RDIs.
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power series A method to derive all the power series through a particular algebraic series
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summation r(r+k) Deriving a general solution for summing the series r(r+k)
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universal calendar Why do you buy a new calendar every year? It's just the same 14 repeated ad infinitum. The trick is figuring out which year has which calendar.
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speeding.pdf Why we should reduce all town speed limits to 20 mph.