Hipparchus explains how two numbers can describe the position of a point on a sphere.
He then explains stereographic projection: how can one draw a picture of the Earth on a piece of paper?
When you look in a mirror, and see what you think is a perfect reflection. You might be looking at a universe whose laws are fundamentally different.
How to predict and model the spread of epidemics.
The SIR model is one of the simplest ways to understand the spread of a disease such as COVID-19 (Coronavirus) through a population. Allowing the movement of populations makes the model slightly more realistic and results in ‘Travelling Wave’ solutions.
The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population.
Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states – simultaneously decayed or not decayed. So is the cat’s wavefunction also in a superposition of both dead and alive.
First, an old idea by Henri Poincaré (1854-1912): when studying a vector field in space, we can sometimes find a small disc that the trajectories hit repeatedly. Studying the points on the disc where the trajectories pass through is often a lot simpler than studying the vector field as a whole. We go from dynamics in continuous time to dynamics in discrete time.
We need two numbers to describe a swinging pendulum: one is its position, the angle versus a vertical line, and the other is its speed, the sign of which indicating that it moves to the right or to the left. Read More