Blog
Are there more even or odd numbers?
Are there more even or odd numbers? And more positive integers or real numbers? How to compare infinite sets using a one-to-one correspondence.
How to calculate vaccine effectiveness
How vaccine effectiveness is calculated and why more vaccinated than unvaccinated people can die. The apparent paradox explained with concrete numbers.
What is 1 + 2 + 5 × 0? On the order of operations
What is 1 + 2 + 5 × 0? Why multiplication takes priority over addition, how to change the order with brackets, and why calculators sometimes give a different answer.
The biggest problem in computer science: P versus NP
The P versus NP problem, one of the seven Millennium Prize Problems with a million-dollar prize. The classes P and NP through examples, and what P = NP would change.
The Trachtenberg method of fast addition
The Trachtenberg method of fast addition for several numbers written one under another. A step-by-step procedure and a clever check of the intermediate results and the final answer.
Philosophical razors
Occam’s razor: when there are two explanations for a phenomenon, we prefer the simpler one. What the principle says, what it does not say and how it is used in science.
Averages
How to calculate average speed from the distance travelled and the time taken. The basic formula, worked examples and conversions between different units.
Mixing and diluting solutions
How to dilute and mix solutions. The concentration of a solution, the mixture equation and how to work out what to add and how much to get the solution you want.
Why we have seasons
Why we have seasons. It is not the distance between the Earth and the Sun, but the tilt of the Earth’s axis and the angle at which the Sun’s rays strike the ground.
The seven bridges of Königsberg
The seven bridges of Königsberg: can you cross every bridge exactly once? A famous problem that Euler solved, founding graph theory in the process.
