# All articles (244)

### A

- A Level and beyond
- About
- Adjacency matrices
- Advanced trigonometry
- Angle at the centre of a circle is twice the angle at the circumference
- Angle in a semicircle is 90 degrees
- Angles in the same segment of a circle are equal
- Area and circumference of circles
- Area and perimeter
- Area and perimeter of quadrilaterals
- Area and perimeter of triangles
- Argand diagrams
- arcosh function
- arsinh function
- artanh function

### B

- Bayes' theorem
- Bifurcation and chaos
- Binary addition, subtraction and negative numbers
- Binary numbers
- Binary numbers
- Binomial distribution
- Boolean algebra

### C

- Calculating a Maclaurin series
- Cantor set
- Cartesian equation of a parabola
- Cartesian equation of a rectangular hyperbola
- Cartesian equation of ellipse
- Cartesian product
- Circle geometry
- Coin rotation paradox
- Collage theorem
- Combinations
- Combining and inverting transform matrices
- Combining logic gates
- Complex number arithmetic
- Complex number trigonometry functions
- Complex numbers
- Complex polynomials
- Complex powers and roots of complex numbers
- Computer science
- Congruent and similar shapes
- Congruent shapes
- Congruent triangles
- Coordinate systems
- Cosine rule
- Countable and uncountable sets
- Creating a subtractor with logic gates
- Creating an adder with logic gates
- Cube
- Cube surface area and net
- cosech function
- cosh function
- coth function

### D

- D-type flip-flops
- De Moivre's theorem
- Decagons - polygons with 10 sides
- Derivative of sine, geometric proof
- Derivative of the exponential function
- Determinants
- Diagonalising matrices
- Differentiation
- Differentiation - L'Hôpital's rule
- Differentiation - derivative of an inverse function
- Differentiation - the chain rule
- Differentiation - the product rule
- Differentiation - the quotient rule
- Differentiation from first principles - a to the power x
- Differentiation from first principles - x²
- Dijkstra's algorithm
- Dodecagons - polygons with 12 sides
- Downloadable classroom resources
- Drawing Sierpinski triangles
- Drunk man and keys problem

### E

- Einstein's proof of Pythagoras' theorem
- Ellipses
- Error page not found
- Escape-time fractals
- Euler's formula - proof
- Exponential and logarithm functions

### F

- Factorials
- Finding arc length by integration
- Formula for e
- Fractal dimension of self-similar fractals
- Fractals
- Fractals
- Fundamental theorem of calculus

### G

- GCSE
- GCSE graphs
- GCSE measures
- Gabriel's horn
- Geometry
- Geometry basic rules
- Gradient of a line
- Graph theory
- GraphicMaths
- Graphs
- Graphs of exponential functions
- Graphs of sloping lines through the origin
- Greatest common divisor (GCD) of two numbers

### H

- Hendecagons - polygons with 11 sides
- Heptagons - polygons with 7 sides
- Hexagons - polygons with 6 sides
- Horizontal, vertical and diagonal straight line graphs
- Hyperbolas
- Hyperbolic angle
- Hyperbolic functions

### I

- Imaginary and complex numbers
- Integration
- Integration by parts
- Integration by parts - LIATE rule
- Integration by substitution
- Interior and exterior angles of a polygon
- Introduction to Fractals
- Introduction to eigenvectors
- Introduction to statistics
- i to the power i

### K

### L

- L system Koch curve
- L system trees and ferns
- L systems
- Lexicographic order
- Line symmetry
- Loci
- Locus of points a fixed distance from a given line
- Locus of points a fixed distance from a given point
- Locus of points an equal distance between 2 lines
- Locus of points an equal distance between 2 points
- Logic
- Logic gates
- Lowest common multiple (LCM) of two numbers

### M

- Maclaurin and Taylor series
- Maclaurin series of the exponential function
- Maclaurin series of the sine function
- Mathematical models in mechanics
- Matrices
- Matrix inverse
- Mean value theorem for integrals
- Mechanics
- Modulus-argument form of complex numbers
- Monty Hall problem
- More quadrilaterals

### N

- Negative and fractional exponents
- Newton Fractal
- Nonagons - polygons with 9 sides
- Normal distribution
- Number theory
- Numerical integration
- Numerical methods
- n-gons - polygons with any number of sides

### O

- Octagons - polygons with 8 sides
- Opposite angles in a cyclic quadrilateral add up to 180°
- Other types of polygon

### P

- Painter's paradox
- Parabola example
- Parabola focus and directrix
- Parabolas
- Parabolas - effect of parameter 'a'
- Paradoxes
- Parallel lines
- Parametric equation of ellipse
- Parametric equations
- Parts of a circle
- Pentagons - polygons with 5 sides
- Permutation matrices and graphs
- Permutations
- Permutations and combinations
- Perpendicular bisector of a chord
- Pi isn't about circles
- Pigeonhole principle
- Polar coordinates
- Polar curve constant r
- Polar curve constant theta
- Polar curve r proportional to theta
- Polygons
- Potato paradox
- Prime factors of a number
- Probability
- Probability distributions
- Proof that e is irrational
- Pure mathematics
- Pythagoras
- Pythagoras' theorem
- Pythagoras' theorem proof
- Pythagorean triples

### Q

### R

- Radians
- Raven paradox
- Recreational maths
- Rectangular hyperbola example
- Regular polygons
- Regular tessellations
- Root 2 is irrational - proof by prime factors
- Rotational symmetry
- Rules of exponents
- Russell's paradox

### S

- Second derivative and sketching curves
- Semiprocal numbers - z to the power i
- Set theory
- Similar shapes
- Similar triangles
- Similar triangles proof
- Simple flip-flops
- Sine rule
- Sleeping Beauty problem
- Slope of a curve
- Solving equations numerically
- Solving equations using interval bisection
- Solving equations using linear interpolation
- Solving equations using the Newton-Raphson method
- Solving simultaneous equations with matrices
- Standard curves in polar coordinates
- Star polygons
- Statistics
- Statistics overview
- Straight line graphs
- Surprise exam paradox
- sech function
- sinh function

### T

- Tangent and radius of a circle meet at 90°
- Tessellations and symmetry
- The seven bridges of Königsberg
- Tools
- Transformations
- Translation
- Travelling salesman problem
- Triangles
- Trigonometry
- Trigonometry and Pythagoras
- Trinary numbers
- Two radii form an isosceles triangle
- Two tangents from a point have equal length
- tanh function

### V

### W

- What is a matrix?
- What is e?
- What is integration
- Why are the trig functions called sine, cosine and tangent?
- Why does complex number multiplication cause rotation?
- Writing a maths book in LaTeX

### Z

### Other

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