All articles (253)



A

  1. A Level and beyond
  2. About
  3. Adjacency matrices
  4. Advanced trigonometry
  5. Angle at the centre of a circle is twice the angle at the circumference
  6. Angle in a semicircle is 90 degrees
  7. Angles in the same segment of a circle are equal
  8. Area and circumference of circles
  9. Area and perimeter
  10. Area and perimeter of quadrilaterals
  11. Area and perimeter of triangles
  12. Area under a polar function
  13. Argand diagrams
  14. arcosh function
  15. arsinh function
  16. artanh function

B

  1. Bayes' theorem
  2. Bifurcation and chaos
  3. Binary addition, subtraction and negative numbers
  4. Binary numbers
  5. Binary numbers
  6. Binomial distribution
  7. Boolean algebra

C

  1. Calculating a Maclaurin series
  2. Cantor set
  3. Cartesian equation of a parabola
  4. Cartesian equation of a rectangular hyperbola
  5. Cartesian equation of ellipse
  6. Cartesian product
  7. Challenging problems
  8. Circle geometry
  9. Coin rotation paradox
  10. Collage theorem
  11. Combinations
  12. Combining and inverting transform matrices
  13. Combining logic gates
  14. Complex number arithmetic
  15. Complex number trigonometry functions
  16. Complex numbers
  17. Complex polynomials
  18. Complex powers and roots of complex numbers
  19. Computer science
  20. Congruent and similar shapes
  21. Congruent shapes
  22. Congruent triangles
  23. Continuous uniform distribution
  24. Coordinate systems
  25. Cosine rule
  26. Countable and uncountable sets
  27. Creating a subtractor with logic gates
  28. Creating an adder with logic gates
  29. Cube
  30. Cube surface area and net
  31. cosech function
  32. cosh function
  33. coth function

D

  1. D-type flip-flops
  2. De Moivre's theorem
  3. Decagons - polygons with 10 sides
  4. Derivative of sine, geometric proof
  5. Derivative of the exponential function
  6. Determinants
  7. Diagonalising matrices
  8. Differentiation
  9. Differentiation - L'Hôpital's rule
  10. Differentiation - derivative of an inverse function
  11. Differentiation - the chain rule
  12. Differentiation - the product rule
  13. Differentiation - the quotient rule
  14. Differentiation from first principles - a to the power x
  15. Differentiation from first principles - x²
  16. Dijkstra's algorithm
  17. Dodecagons - polygons with 12 sides
  18. Downloadable classroom resources
  19. Drawing Sierpinski triangles
  20. Drunk man and keys problem

E

  1. Einstein's proof of Pythagoras' theorem
  2. Ellipses
  3. Error page not found
  4. Escape-time fractals
  5. Euler's formula - proof
  6. Exponential and logarithm functions

F

  1. Factorials
  2. Factors of a prime squared minus 1
  3. Finding arc length by integration
  4. Formula for e
  5. Fractal dimension of self-similar fractals
  6. Fractals
  7. Fractals
  8. Fundamental theorem of calculus

G

  1. GCSE
  2. GCSE graphs
  3. GCSE measures
  4. Gabriel's horn
  5. Geometry
  6. Geometry basic rules
  7. Gradient of a line
  8. Graph theory
  9. GraphicMaths
  10. Graphs
  11. Graphs of exponential functions
  12. Graphs of sloping lines through the origin
  13. Greatest common divisor (GCD) of two numbers

H

  1. Hendecagons - polygons with 11 sides
  2. Heptagons - polygons with 7 sides
  3. Hexagons - polygons with 6 sides
  4. Horizontal, vertical and diagonal straight line graphs
  5. Hyperbolas
  6. Hyperbolic angle
  7. Hyperbolic functions

I

  1. Imaginary and complex numbers
  2. Improper integrals
  3. Integration
  4. Integration by parts
  5. Integration by parts - LIATE rule
  6. Integration by substitution
  7. Interior and exterior angles of a polygon
  8. Introduction to Fractals
  9. Introduction to eigenvectors
  10. Introduction to statistics
  11. i to the power i

K

  1. Koch snowflake

L

  1. L system Koch curve
  2. L system trees and ferns
  3. L systems
  4. Lexicographic order
  5. Line symmetry
  6. Loci
  7. Locus of points a fixed distance from a given line
  8. Locus of points a fixed distance from a given point
  9. Locus of points an equal distance between 2 lines
  10. Locus of points an equal distance between 2 points
  11. Logic
  12. Logic gates
  13. Lowest common multiple (LCM) of two numbers

M

  1. Maclaurin and Taylor series
  2. Maclaurin series of the exponential function
  3. Maclaurin series of the sine function
  4. Mathematical models in mechanics
  5. Matrices
  6. Matrix inverse
  7. Mean value theorem for integrals
  8. Mechanics
  9. Modulus-argument form of complex numbers
  10. Monty Hall problem
  11. More quadrilaterals

N

  1. Negative and fractional exponents
  2. Newton Fractal
  3. Nonagons - polygons with 9 sides
  4. Normal distribution
  5. Number theory
  6. Numerical integration
  7. Numerical methods
  8. n-gons - polygons with any number of sides

O

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

P

  1. Painter's paradox
  2. Parabola example
  3. Parabola focus and directrix
  4. Parabolas
  5. Parabolas - effect of parameter 'a'
  6. Paradoxes
  7. Parallel lines
  8. Parametric equation of ellipse
  9. Parametric equations
  10. Parts of a circle
  11. Pentagons - polygons with 5 sides
  12. Permutation matrices and graphs
  13. Permutations
  14. Permutations and combinations
  15. Perpendicular bisector of a chord
  16. Pi isn't about circles
  17. Pigeonhole principle
  18. Polar coordinates
  19. Polar curve constant r
  20. Polar curve constant theta
  21. Polar curve r proportional to theta
  22. Polygons
  23. Potato paradox
  24. Prime factors of a number
  25. Probability
  26. Probability distributions
  27. Proof that e is irrational
  28. Pure mathematics
  29. Pythagoras
  30. Pythagoras' theorem
  31. Pythagoras' theorem proof
  32. Pythagorean triples

Q

  1. Quadrilateral family tree
  2. Quadrilaterals

R

  1. Radians
  2. Raven paradox
  3. Recreational maths
  4. Rectangular hyperbola example
  5. Regular polygons
  6. Regular tessellations
  7. Root 2 is irrational - proof by prime factors
  8. Rotational symmetry
  9. Rules of exponents
  10. Russell's paradox

S

  1. Second derivative and sketching curves
  2. Semiprocal numbers - z to the power i
  3. Set theory
  4. Similar shapes
  5. Similar triangles
  6. Similar triangles proof
  7. Simple flip-flops
  8. Sine rule
  9. Sleeping Beauty problem
  10. Slope of a curve
  11. Solving equations numerically
  12. Solving equations using interval bisection
  13. Solving equations using linear interpolation
  14. Solving equations using the Newton-Raphson method
  15. Solving simultaneous equations with matrices
  16. Special functions
  17. Standard curves in polar coordinates
  18. Star polygons
  19. Statistics
  20. Statistics overview
  21. Straight line graphs
  22. Surprise exam paradox
  23. sech function
  24. sinh function

T

  1. Tangent and radius of a circle meet at 90°
  2. Tessellations and symmetry
  3. The golden ratio
  4. The pi function
  5. The seven bridges of Königsberg
  6. Tools
  7. Transformations
  8. Translation
  9. Travelling salesman problem
  10. Triangles
  11. Trigonometry
  12. Trigonometry and Pythagoras
  13. Trinary numbers
  14. Two radii form an isosceles triangle
  15. Two tangents from a point have equal length
  16. tanh function

V

  1. Videos
  2. Volume of revolution

W

  1. What is a matrix?
  2. What is e?
  3. What is integration
  4. Why are the trig functions called sine, cosine and tangent?
  5. Why does complex number multiplication cause rotation?
  6. Writing a maths book in LaTeX

Z

  1. Zermelo-Fraenkel set theory

Other

  1. 2 to the power π - exponential function for an irrational value of x
  2. 2D transformation matrices
  3. 3D geometry


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