Course: Maths for Humans: Linear, Quadratic & Inverse Relations

Isaac Newton was a giant of modern science, and one of the key architects of the modern world. One of his major insights was that the force of gravitational attraction …

Jakob Steiner was a prominent Swiss geometer who made many remarkable contributions to mathematics. In 1826 he asked: what is the maximum number of regions you could divide the plane …

The study of how things scale in biology, usually with respect to body size, is called allometry. The term was introduced by Huxley & Tessier in 1936 in their study …

In this video we discuss other kinds of relations going beyond the elementary polynomial and power laws, culminating with a formula of Cayley on the number of labelled trees on …

In 1609 Kepler formulated his first two laws to summarize the remarkable astronomical observations his mentor Tycho Brahe had made over many years. Ten years later he published his third …

It has been observed that the heartrate and metabolic rate per cell is less for large animals, and greater for small animals. All well and good, but having some equations …

Kleiber’s law was proposed by Max Kleiber, a Swiss chemist, in the 1930’s. The idea is to try to quantify the relation between how big an animal is, and what …

More than a hundred years ago, the Italian economist Vilfredo Pareto (1848- 1923) studied income and wealth distributions. And he noted a curious fact: that certain power laws seemed to …

In this video we explain the mathematical power laws that relate animal mass to heart rate and lifespan. Allometry In biology, the application of power laws is part of allometry, …

What is the relationship between the size of an animal and how long it lives? This interesting topic raises lots of questions, many quite pertinent to our modern lives. It …

Sometimes in real life we have data that does not fit into our preconceived patterns or formulas. There are so many questions we can ask about the modern world: it …

It is commonly accepted that regular exercise adds years onto life, but what exactly is the power of exercise? And is this power a power law? In this step, we …

A power law relation has the form \(\normalsize{y=ax^k}\) for some number \(\normalsize{k}\), not necessarily an integer. In this video we introduce this more general kind of relation, explain how the …

The larger a city is, the more gas stations it will have. On average, there ought to be some kind of quantitative relationship between the number of gas stations \(\normalsize{G}\), …

Just as for quadratic functions, knowing the zeroes of a cubic makes graphing it much simpler. Typically a cubic function will have three zeroes or one zero, at least approximately, …