Most recent 261 articles

Jan 2025

1. How carbon dating works
2. Science and philosophy
3. Physics

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. What is nothing? Kuhn's nine levels of nothing
2. Improper integrals
3. De Moivre's theorem
4. Challenging problems
5. Factors of a prime squared minus 1
6. Continuous uniform distribution
7. Integration by parts
8. Differentiation - derivative of an inverse function
9. The pi 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. Normal distribution
4. Probability distributions
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. Introduction to Fractals
2. Fractal dimension of self-similar 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. Probability
10. Bayes' theorem

Oct 2023

1. Bifurcation and chaos
2. Creating an adder with logic gates
3. Matrices
4. What is a matrix?
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 gates
6. Logic
7. Euler's formula - proof
8. Cantor set
9. Trinary numbers
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. Paradoxes
4. Monty Hall problem
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. Differentiation
2. Slope of a curve
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. Graphs of exponential functions
5. Negative and fractional exponents
6. Rules of 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 shapes
5. Congruent and similar shapes
6. Tangent and radius of a circle meet at 90°

Nov 2022

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

Oct 2022

1. Area and perimeter of triangles
2. Star polygons
3. Area and perimeter
4. Other types of polygon
5. Triangles
6. Pentagons - polygons with 5 sides
7. Dodecagons - polygons with 12 sides
8. Octagons - polygons with 8 sides
9. Decagons - polygons with 10 sides
10. Hendecagons - polygons with 11 sides
11. Hexagons - polygons with 6 sides
12. Heptagons - polygons with 7 sides
13. Nonagons - polygons with 9 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. Horizontal, vertical and diagonal straight line graphs
3. Graphs of sloping lines through the origin
4. GCSE 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. Maclaurin and Taylor series
4. Lowest common multiple (LCM) of two numbers
5. Greatest common divisor (GCD) of two numbers
6. Number theory
7. Prime factors of a number
8. Exponential and logarithm functions
9. Radians
10. Advanced trigonometry

Nov 2021

1. Mechanics
2. Mathematical models in mechanics
3. Cartesian product
4. Combinations
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. sech function
5. cosech function

Jan 2021

1. Trigonometry and Pythagoras
2. Sine rule

Sep 2020

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

Aug 2020

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

Mar 2020

1. About
2. Pure mathematics

Feb 2020

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