by Jo Boaler
I love numbers. One of the things I most love about them is the interesting ways they are made and the ways they combine together to reveal fascinating and seemingly endless patterns.
Many people think of numbers as European creations – but they have a rich, cultural history that draws from different regions of the world.
Caleb Everett, a cognitive linguist, writes in his fascinating book: Numbers and the Making of Us that some of the first quantitative records were found in the Brazilian Amazon. And the first awareness of base 12, prime numbers, and the decimal system was recorded in the Congolese area of Africa. The first users of algebra, and geometry were the Sumerians and Babylonians and today’s Western number system – came from the Arabic system – which in turn came from the Indian number system. The history of number is culturally rich and fascinating.
Something else that I love about numbers – did you know that their names often tell you how they are constructed? I am amazed (saddened) by the number of people who do not know that square numbers are called square numbers because they can be shown as a square.
And even more people have not heard of triangular numbers – the numbers that make triangles.
And did you know that if you add consecutive odd numbers they make square numbers?
I love all of these characteristics of numbers, and one of my favorite youcubed activities is the exploration of number visuals that you can find here.
I recently learned about some other interesting number names when reading Ben Orlin’s new book: Math Games with Bad Drawings.
In the book he introduces “perfect numbers”. A perfect number is one where the factors of the number added up make the number. Six is a perfect number as the factors are 1, 2 and 3, which add up to 6. Ben shows 3 perfect numbers here:
(Orlin, 2022, p 84)
Then there are some very cutely named “amicable numbers.” Numbers are amicable when adding up the factors takes you to a different number, and adding up those factors takes you back to the original number. For example 220 sends you to 284, who sends you right back to 220. So 220 and 284 are amicable numbers.
Apparently mathematicians spent years trying to find other amicable numbers, until the next 2 (1184 and 1210) were discovered by a 16 year old called Nicolò Paganini. Today over a billion pairs of amicable numbers have been discovered.
You are probably beginning to understand why I love numbers. Over the next few months I will share more of my love for them.
And if you would like to read the books I quoted in this blog post, here they are:
Everett, C. (2017). Numbers and the Making of Us. In Numbers and the Making of Us. Harvard University Press.
&
Orlin, B. (2022). Math Games with Bad Drawings. Black Dog & Leventhal
