Most recent 257 articles

Dec 2024

1. Pathological cases - Dirichlet function
2. Limits
3. Squeeze theorem

Nov 2024

1. generativepy documentation

Oct 2024

1. Volume of revolution

Sep 2024

1. Surprise exam paradox
2. Zermelo-Fraenkel set theory

Aug 2024

1. Integration by parts - LIATE rule
2. The golden ratio
3. Numerical integration

Jul 2024

1. Improper integrals
2. De Moivre's theorem
3. Factors of a prime squared minus 1
4. Challenging problems
5. Continuous uniform distribution
6. Integration by parts
7. The pi function
8. Differentiation - derivative of an inverse function

Jun 2024

1. Area under a polar function
2. Statistics overview
3. Special functions
4. Finding arc length by integration
5. Permutation matrices and graphs
6. Proof that e is irrational

May 2024

1. Sleeping Beauty problem
2. Writing a maths book in LaTeX
3. Tools
4. Combining and inverting transform matrices
5. Fundamental theorem of calculus
6. Diagonalising matrices

Apr 2024

1. Binomial distribution
2. Introduction to eigenvectors
3. Probability distributions
4. Normal distribution
5. Downloadable classroom resources

Mar 2024

1. Russell's paradox
2. Introduction to statistics
3. Solving simultaneous equations with matrices
4. Creating a subtractor with logic gates
5. Complex number trigonometry functions
6. Root 2 is irrational - proof by prime factors

Feb 2024

1. Fractal dimension of self-similar fractals
2. Introduction to Fractals
3. Koch snowflake
4. Gabriel's horn
5. Mean value theorem for integrals

Jan 2024

1. Coin rotation paradox
2. Second derivative and sketching curves
3. Complex polynomials
4. Raven paradox
5. L system Koch curve
6. Boolean algebra
7. 2D transformation matrices
8. Imaginary and complex numbers

Dec 2023

1. Differentiation - L'Hôpital's rule
2. Potato paradox
3. Matrix inverse
4. Differentiation from first principles - a to the power x
5. Integration by substitution
6. D-type flip-flops

Nov 2023

1. Determinants
2. Painter's paradox
3. What is integration
4. Integration
5. Travelling salesman problem
6. Differentiation - the quotient rule
7. Semiprocal numbers - z to the power i
8. Simple flip-flops
9. Bayes' theorem
10. Probability

Oct 2023

1. Bifurcation and chaos
2. Creating an adder with logic gates
3. What is a matrix?
4. Matrices
5. Pi isn't about circles
6. Dijkstra's algorithm
7. Combining logic gates
8. Complex powers and roots of complex numbers
9. The seven bridges of Königsberg

Sep 2023

1. Binary addition, subtraction and negative numbers
2. Differentiation - the chain rule
3. Drunk man and keys problem
4. Hyperbolic angle
5. Logic
6. Logic gates
7. Euler's formula - proof
8. Trinary numbers
9. Cantor set
10. Derivative of sine, geometric proof

Aug 2023

1. Binary numbers
2. Binary numbers
3. Adjacency matrices
4. Countable and uncountable sets
5. Set theory
6. i to the power i
7. Differentiation - the product rule

Jul 2023

1. Modulus-argument form of complex numbers
2. Pigeonhole principle
3. Angles in the same segment of a circle are equal
4. Argand diagrams
5. Pythagorean triples

Jun 2023

1. A Level and beyond
2. Recreational maths
3. Monty Hall problem
4. Paradoxes
5. Drawing Sierpinski triangles
6. Fractals
7. L system trees and ferns
8. L systems

May 2023

1. Opposite angles in a cyclic quadrilateral add up to 180°
2. Collage theorem
3. Computer science
4. Graphs
5. Graph theory
6. Why does complex number multiplication cause rotation?
7. Regular tessellations

Apr 2023

1. Fractals
2. Newton Fractal
3. Escape-time fractals
4. Why are the trig functions called sine, cosine and tangent?
5. Differentiation from first principles - x²

Mar 2023

1. Slope of a curve
2. Differentiation
3. 2 to the power π - exponential function for an irrational value of x
4. Similar triangles proof
5. Cosine rule
6. Similar triangles

Feb 2023

1. Similar shapes
2. Einstein's proof of Pythagoras' theorem
3. Angle at the centre of a circle is twice the angle at the circumference
4. Rules of exponents
5. Graphs of exponential functions
6. Negative and fractional exponents

Jan 2023

1. Parabola focus and directrix
2. Two radii form an isosceles triangle
3. Pythagoras' theorem proof
4. Pythagoras
5. Pythagoras' theorem
6. Rotational symmetry
7. Angle in a semicircle is 90 degrees

Dec 2022

1. Cube
2. Two tangents from a point have equal length
3. Congruent triangles
4. Congruent and similar shapes
5. Congruent shapes
6. Tangent and radius of a circle meet at 90°

Nov 2022

1. Line symmetry
2. Tessellations and symmetry
3. GCSE measures
4. Quadrilateral family tree
5. Area and perimeter of quadrilaterals
6. Maclaurin series of the sine function
7. Maclaurin series of the exponential function
8. Calculating a Maclaurin series
9. Quadrilaterals
10. n-gons - polygons with any number of sides
11. GraphicMaths
12. Area and circumference of circles

Oct 2022

1. Area and perimeter of triangles
2. Area and perimeter
3. Star polygons
4. Other types of polygon
5. Triangles
6. Hendecagons - polygons with 11 sides
7. Dodecagons - polygons with 12 sides
8. Hexagons - polygons with 6 sides
9. Decagons - polygons with 10 sides
10. Octagons - polygons with 8 sides
11. Pentagons - polygons with 5 sides
12. Nonagons - polygons with 9 sides
13. Heptagons - polygons with 7 sides

Sep 2022

1. Translation
2. Interior and exterior angles of a polygon
3. Parts of a circle
4. Factorials

Aug 2022

1. Solving equations using the Newton-Raphson method
2. Derivative of the exponential function
3. Formula for e
4. What is e?

May 2022

1. Gradient of a line
2. Graphs of sloping lines through the origin
3. GCSE graphs
4. Horizontal, vertical and diagonal straight line graphs
5. Straight line graphs
6. Videos
7. Trigonometry

Apr 2022

1. Regular polygons
2. Geometry basic rules

Jan 2022

1. Complex number arithmetic
2. Complex numbers
3. Exponential and logarithm functions
4. Lowest common multiple (LCM) of two numbers
5. Greatest common divisor (GCD) of two numbers
6. Prime factors of a number
7. Number theory
8. Maclaurin and Taylor series
9. Radians
10. Advanced trigonometry

Nov 2021

1. Mechanics
2. Mathematical models in mechanics
3. Combinations
4. Cartesian product
5. Lexicographic order

Oct 2021

1. Permutations
2. Statistics
3. Permutations and combinations

Apr 2021

1. Solving equations using linear interpolation
2. Solving equations using interval bisection

Mar 2021

1. Solving equations numerically
2. Numerical methods

Feb 2021

1. Cube surface area and net
2. 3D geometry
3. coth function
4. cosech function
5. sech function

Jan 2021

1. Sine rule
2. Trigonometry and Pythagoras

Sep 2020

1. Polar curve constant r
2. Polar curve constant theta
3. Polar curve r proportional to theta
4. Polar coordinates
5. Standard curves in polar coordinates
6. Parametric equation of ellipse
7. Cartesian equation of ellipse
8. Ellipses
9. Hyperbolas
10. Parabolas - effect of parameter 'a'
11. Cartesian equation of a rectangular hyperbola
12. Parametric equations
13. Parabolas
14. Cartesian equation of a parabola
15. Parabola example
16. Coordinate systems
17. Rectangular hyperbola example
18. tanh function
19. cosh function
20. sinh function
21. Hyperbolic functions

Aug 2020

1. Transformations
2. Locus of points a fixed distance from a given line
3. Locus of points an equal distance between 2 lines
4. Loci
5. Locus of points a fixed distance from a given point
6. Locus of points an equal distance between 2 points
7. Perpendicular bisector of a chord
8. Parallel lines
9. More quadrilaterals
10. Error page not found
11. Polygons
12. Circle geometry
13. Geometry
14. GCSE

Mar 2020

1. About
2. Pure mathematics

Feb 2020

1. artanh function
2. arcosh function
3. arsinh function