I was asked yesterday, why do they teach the multiplication tables in school. Wasn’t sure whether this was common knowledge, but here’s how it goes. Once you know how to multiply the numbers from 1 to 9 with each other, you can multiply basically any two numbers by hand; doesn’t matter how many digits they have.
Let’s say you want to multiply 132 × 18. When you learn your times-tables, these numbers are not covered. But there is a method for you to follow that will just involve multiplying numbers less than 10. It does assume that you know how to add, but learning how to add numbers with several digits is not that hard either.
There’s more than one way to do multi-digit multiplication, but you can find the descriptions here: https://en.wikipedia.org/wiki/Multiplication_algorithm.
Of course, youtube has a few demonstrations too, for example:
So, 132 × 18 = 2,376. You would be multiplying these numbers on the way: 2 × 1, 3 × 1, 1 × 1, 2 × 8, 3 × 8 and 1 × 8 (which are all really simple!)
Now if you ask why to learn how to multiply numbers in the first place? I find mulitplication comes up quite a lot just in ordinary tasks, doubling baking recipes, find distance from velocity and time, and vice versa, buying quantities of various items. Sometimes I use a calculator, or spread sheet, but often it’s good to do without. There’s lots of different applications!
A finishing carpenter friend of mine recommended I try to use Pythagoras’ Theorem when I asked him, out of desperation, for advice on a difficult math problem that I am stuck on.
When I reported no progress, he asked what other topics in math are named after people, after all, Pythagoras lived a long time ago.
So here’s a very simple list (for now not even in a good order). Please use the links to learn more about what is being named.
- Algorithm, denoting a method of calculation, is named after Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī (Algorithm being his name in Latin). Basic example is the Euclidean algorithm, to calculate the greatest common divisor (of two or more numbers).
- Fibonacci numbers, or Fibonacci sequence, named after Leonardo Pisano Bigollo, also called Leonardo Fibonacci. Each number in the sequence is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
- The Euler number, the base of the natural logarithms, is named after Leonard Euler. Often just “e”: 2.71828… Much more in the world of math is named Euler.
- Cartesian coordinate system, named after René Descartes. The grid with axes, usually called x and y.
- The Bernoulli numbers, are named after Jakob Bernoulli. They appear in series expansions of trigonometric functions.
- Fermat’s theorem, named after Pierre de Fermat. A method for finding maxima and minima of functions.
- Pascal’s triangle, named after Blaise Pascal. The triangle arranges the binomial coefficients.
- Taylor series are named after Brook Taylor. These series represent mathematical functions as infinite sums of simple terms.
- Newton’s method, also, called Newton–Raphson method, named after Isaac Newton, and Joseph Raphson. Method to approximate a zero of a function.
- Galois theory, named after Évariste Galois. Allows proving such things as why there is no formula for the roots of a fifth degree polynomial equation, or why it is not possible to trisect all angles using a compass and straightedge.
- The Lagrangian, named after Joseph Lagrange. Functions that describe how dynamical systems change over time. More in maths is named Lagrange
- Dirichlet’s principle, named after Johann Dirichlet. If you have more items than containers, and distribute all items among the containers, then one container will have more than one item.
- Gaussian elimination, named after Card Friedrich Gauss. An algoritm (see above) for solving systems of linear equations.
- Hamiltonian path, named after William Hamilton. A path in a graph that visits each vertex exactly once.
- Riemann sum, named after Bernhard Riemann. Method for approximating areas given by a curve. Much more in math is named Riemann.
- Hilbert’s Nullstellensatz, named after David Hilbert. Connecting algebra and geometry.
- Turing machines, named after Alan M. Turing. A simple reference model for computation.
There are many, many more, especially from the last century. For example, I left out the Tutte Graph. Wikipedia has a list of things named after mathematicians, however it is still far from complete.
To finish, I’ll list one of a different kind: the Erdős number is the distance to Paul Erdős in terms of coauthorship. (My Erdős number presently is 4)