Most recent 223 articles

Oct 2025

1. Finding the normal to a curve
2. Derivative of ln x
3. Formula for e
4. Derivative of tangent

Sep 2025

1. Which is bigger e^pi or pi^e?
2. The imaginary error function, erfi
3. The gamma function
4. The Gaussian integral

Aug 2025

1. Limits that fail L'Hôpital's rule
2. Finding the speed of light
3. Line symmetry
4. Root 2 is irrational - proof by the carpets theorem
5. Pentagons - polygons with 5 sides
6. Adjacency matrices
7. The erf function
8. Euler's formula and its proof
9. What is e?
10. Space-filling curves
11. Regular tessellations

Jul 2025

1. Countable and uncountable sets
2. Algebraic and transcendental numbers
3. Differentiation - the chain rule (proof)
4. arcosh function
5. arsinh function
6. artanh function
7. Basel problem
8. Sum of square roots (Romanian Olympiad)
9. Galileo's paradox

Jun 2025

1. Two envelope paradox

May 2025

1. The Lambert W function
2. markdown-pdf

Apr 2025

1. 100 prisoners problem
2. Sine rule
3. Vector drawing with generativepy
4. Introduction to generativepy
5. Finding sides and angles with sine, cosine and tangent
6. Distance between two points on a graph
7. Pythagoras' theorem
8. Angle at the centre of a circle is twice the angle at the circumference
9. Angle in a semicircle is 90°

Mar 2025

1. Perpendicular bisector of chord theorem

Feb 2025

1. Alternate segment theorem
2. Parts of a circle
3. Tangent and radius of a circle meet at 90°
4. Python walrus operator

Jan 2025

1. How carbon dating works

Dec 2024

1. Pathological cases - Dirichlet function
2. Squeeze theorem

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. Factors of a prime squared minus 1
5. Continuous uniform distribution
6. Integration by parts
7. Differentiation - derivative of an inverse function
8. The pi function

Jun 2024

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

May 2024

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

Apr 2024

1. Binomial distribution
2. Introduction to eigenvectors
3. Normal distribution

Mar 2024

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

Feb 2024

1. Fractal dimension of self-similar fractals
2. Koch snowflake
3. Gabriel's horn
4. 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. Travelling salesman problem
5. Differentiation - the quotient rule
6. Semiprocal numbers - z to the power i
7. Simple flip-flops
8. Bayes' theorem

Oct 2023

1. Bifurcation and chaos
2. Creating an adder with logic gates
3. What is a matrix?
4. Pi isn't about circles
5. Dijkstra's algorithm
6. Combining logic gates
7. Complex powers and roots of complex numbers
8. 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. Cantor set
7. Trinary numbers
8. Derivative of sine, geometric proof

Aug 2023

1. Binary numbers
2. i to the power i
3. 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. Monty Hall problem
2. Drawing Sierpinski triangles
3. L system trees and ferns

May 2023

1. Opposite angles in a cyclic quadrilateral add up to 180°
2. Graphs
3. Why does complex number multiplication cause rotation?

Apr 2023

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

Mar 2023

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

Feb 2023

1. Similar shapes
2. Einstein's proof of Pythagoras' theorem
3. Graphs of exponential functions
4. Negative and fractional exponents
5. Rules of exponents

Jan 2023

1. Parabola focus and directrix
2. Two radii form an isosceles triangle
3. Pythagoras' theorem proof
4. Rotational symmetry

Dec 2022

1. Cube
2. Two tangents from a point have equal length
3. Congruent triangles
4. Congruent shapes

Nov 2022

1. Quadrilateral family tree
2. Area and perimeter of quadrilaterals
3. Maclaurin series of the sine function
4. Maclaurin series of the exponential function
5. Calculating a Maclaurin series
6. n-gons - polygons with any number of sides
7. Quadrilaterals
8. Area and circumference of circles

Oct 2022

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

Sep 2022

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

Aug 2022

1. Solving equations using the Newton-Raphson method
2. Derivative of the exponential function

May 2022

1. Gradient of a line
2. Horizontal, vertical and diagonal straight line graphs
3. Graphs of sloping lines through the origin

Apr 2022

1. Regular polygons

Jan 2022

1. Complex number arithmetic
2. Greatest common divisor (GCD) of two numbers
3. Lowest common multiple (LCM) of two numbers
4. Prime factors of a number
5. Radians

Nov 2021

1. Cartesian product
2. Combinations
3. Lexicographic order

Oct 2021

1. Permutations

Apr 2021

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

Mar 2021

1. Solving equations numerically

Feb 2021

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

Sep 2020

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

Aug 2020

1. Locus of points an equal distance between 2 lines
2. Locus of points an equal distance between 2 points
3. Locus of points a fixed distance from a given line
4. Locus of points a fixed distance from a given point