Online maths video

Symbols used

**Methods/heuristics/principles** (under construction)

**Sequences**

Golden ratio and Fibonacci sequence

the Thue-Morse sequence

Farey sequence – under construction

root sequence – under construction

**Triangles, geometry, trigonometry**

sin, cos, tan etc – under construction

**Polynomials**

Ruffini’s rule/synthetic division/Horner’s form/Horner’s method etc

Lill’s method of finding roots graphically

**Quadratic equations etc** (under construction)

Finding 2 numbers from their product and sum

the quadratic formula

The discriminant and the roots of a quadratic equation

symmetric functions

**Series**

**Sums** of powers of integers, finding sums

Jakob Bernoulli’s power sum problem and Bernoulli numbers – see also method of undetermined coefficients

Calculus vs **Finite calculus, and falling powers**

table of differences and sums

some applications of finite calculus

telescoping series (under construction)

geometric series

some simple series illustrated

the harmonic series

p-series

Riemann zeta function

tests for series convergence/divergence (under construction)

**Power series**

power series, transcendental functions, interpolation etc – historical (under construction)

Maclaurin and Taylor series, series for e, sin etc

Kummer’s method

power series convergence/divergence (under construction)

**series acceleration**

– **linear transformations**

Euler transformation

what wikipedia calls ‘van Wijngaarden transformation’ (which isn’t)

– **non-linear transformations**

Padé approximants

Aitken’s process

Shanks transformation

Wynn’s method

Levin transformations

**Generating functions**

User-unfriendly guide to Generating functions

Some basic sequences, generating functions, closed forms

**Products**

telescoping products (under construction)

Stirling’s approximation of n! (under construction)

**Continued fractions etc**

Euclid’s algorithm = continued fractions = squares in a rectangle

The magic table method of finding convergents (under construction)

Combinatorial interpretation of CFs

How to calculate the continued fraction of (unfinished)

Gallery of continued fractions

sums and continued fractions – for

Finding a CF for a given sequence of approximants

Formulas for CFs

common functions as CFs

Series and CFs

CF equivalence transformations

Fractions constructible with different-sized squares (under construction 🙂 )

3D Euclidean jigsaw method (under construction)

some applications of CFs (under construction)

3D CFs

Pics of CFs

**Calculus**

A picture of differentiation

Differentiation rules and standard derivatives

integration by parts

series and definite integral

**Number theory etc**

modular arithmetic

Modular arithmetic & residues – Pictures of possible values of

The binomial theorem

the arithmetic, geometric and harmonic mean and the AMGM inequality

the exponential inequality

Fermat’s (little) theorem

a picture of Fermat’s last theorem

pictures of Primes and prime factors

Euclid, perfect numbers and Mersenne primes

Euler’s phi (totient) function

The Fermat-Euler Theorem

Wilson’s theorem

Euler’s number e

Euler’s number

**Dynamical systems, fractals, chaos**

Mandelbrot set

to add: – lectures/courses/talks – Prisoner’s dilemma, game theory – RBMs, neural nets – knots – chords, codes – prime formulae – origami – squared rectangles/squares, circuits, graphs – curves, fractals, interpolation – analytic & harmonic complex functions

Bernoulli numbers, Catalan numbers, Lucas numbers, Stern-Brocot tree, Calkin-Wilf tree, squaring rectangles/squares = electric circuit theory, cellular automata

**my stuff
**Squaring the plane II

Squaring the plane

phinary

chess board equations – board designs (Is this maths or art?! Game design? All 3 I guess.)

and operators –

my areas of interest (under construction)