Blog

Maya numbers

David Shaw

7 March, 2017

An excerpt from the Dresden Codex, including some Maya numbers.

The numbers that we use are not the only way to write numbers. You might know how to count with tally marks, or read Roman numerals. But there are plenty of other ways to write numbers. This one comes from the Maya people.

You will need

Pen and paper

What to do

some maya number symbols, including dot, dot equals 2 and dot line equals six.

Let’s start at the start. To write a 1, simply draw a dot!
The numbers 2, 3 and 4 are equally easy – just put the right number of dots, sideways in a row.
The number 5 is a horizontal line. To make 6 to 9, put dots above the line.
To make 10, put a second horizontal line below the first. You can add dots to make the numbers 11–14, a third line to make 15, and more dots to make 16–19.
To write zero, draw a shell shape.
Here’s where it gets interesting! Our number system is based on 10, which is written as a 1 and a 0. Maya numbers are based around the number 20, so in Maya numbers, 20 is a 1 and a 0. So write a dot for the 1 and leave a gap below it. Then below the gap, draw a clamshell – the Mayan symbol for zero.
To write numbers from 21–39, think of them as 20 plus something. For example, 31 is 20 + 11, so draw a dot, then a gap, then a dot and two lines (11 in Mayan!).
A Maya 20: the shell is in the ones place, so the dot is in the twenties place!
To write numbers up to 399, think of the number as ‘some 20s + something’. For example, 165 is eight 20s, plus five. To write this, draw three dots and a line (8), then a gap, and finally a line (5).
399 is nineteen 20s plus 19, which makes it the largest number you can write with two Mayan ‘digits’. To write 400, think of it as twenty 20s. So 400 is written as a dot, a gap, a clamshell, a gap and a second clamshell.
The single dot is in the twenties place, and the 11 is in the ones place, so this number is 31.

What’s happening?

The remarkable Maya civilisation lasted for thousands of years, until they were conquered by the Spanish more than 300 years ago. They invented a full written language, and also had an advanced number system.

A dot over a shell over a shell is 400. A dot over a shell over a dot is 401.

Although it looks basic – almost like tally marks – the Maya number system is very sophisticated. It is one of the oldest number systems with a zero. This symbol dates back to at least 36 BCE, when the Roman Empire was still using Roman numerals.

You might have some difficulty using Maya numbers, because they are based around the number 20 rather than the number 10. But there’s actually no reason why our 10-based system is easier to use. You only find our numbers easier because that’s what you were taught!

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Categories:

Hands-on, Maths

Tags:

counting, ethnomathematics, mathematical sciences, Maya, number, number systems, roman numerals

19 responses

Hi

9 December, 2019

I do it a bit differently to that when I do the set out of the symbol

Reply
1. David
  
  9 December, 2019
  
  Hi Hi,
  Yup, there are probably many different ways to write these numbers – they were used over a large area for over a thousand years.
  
  If you look at old textbooks, such as Fibonacci’s Liber Abaci, you’ll notice some of the numerals are completely the wrong shape! our 1234567890 shapes are only about 500 years old!
  
  Reply
Don’t need to know

9 December, 2019

What about over 2 thousand?

Reply
1. David
  
  9 December, 2019
  
  Hi Don’t,
  Just like with our number system, you can keep counting by adding more digits to the front of the number. Only with Mayan numbers, the next digit goes on top!
  This activity explores the ones, twenties and four hundreds digits. If you put a fourth digit on top, it’s in the eight thousands place- so dot, shell, shell, shell is eight thousand!
  
  Reply
Dominic Evans

25 December, 2019

I have a theory on how the Mayan might have used their fingers to count to 20. I made a video. What do you think?

https://youtu.be/GQTTM_ZMmvI

Reply
Sev

6 March, 2020

What is the largest number that can be counted to, in a vigesimal
system with four places

Reply
1. David
  
  7 March, 2020
  
  It’s probably the value of the smallest 5 digit number, minus 1!
  
  Reply
Ma’Nya

10 March, 2020

COOL COOL I did not know that

Reply
Gabriel Negumbo

20 March, 2020

Hi… I have a question;
What is the largest number that can be counted to, in a vigesimal (base-20) system with four places? Please write the answer using numeric digits only.

Reply
1. David
  
  20 March, 2020
  
  The largest four digit number is just a bit smaller than the smallest five digit number. So work that out, and count backwards to get your answer!
  
  Reply
Jorge Acosta

17 September, 2020

How would you write 2020?

Reply
1. David
  
  17 September, 2020
  
  Hi Jorge,
  We’ll need to write 2020 in terms of 400, 20 and 1:
  2020 = 5 x 400 + 1 x 20 + 0 x 1
  then we convert to symbols:
  horizontal line = 5, dot = 1, shell = 0
  and that’s the answer – horizontal line, gap, dot, gap, shell.
  
  Reply
Jim

23 October, 2020

why don’t you have twelve and eight

Reply
Kro

22 January, 2021

Do you have copyable Mayan numerals? Like ones I can copy and paste of a document, that aren’t a image.

Reply
1. David
  
  22 January, 2021
  
  you can grab some images of numerals on wikipedia:
  https://en.wikipedia.org/wiki/Maya_numerals
  
  if you have the right font installed (I don’t know which one you need sadly), you could use these unicode characters:
  https://en.wikipedia.org/wiki/Mayan_Numerals_(Unicode_block)
  
  hope this helps!
  
  Reply
Me

27 July, 2021

What about 1000?

Reply
1. David
  
  27 July, 2021
  
  Hi there!
  1000 is two 400s, plus ten 20s, plus zero. so it should appear as:
  2 dots, 2 lines, shell.
  
  Reply
Sienna

14 March, 2022

Can you pls do an example for 499 and 45.

Reply
1. David
  
  15 March, 2022
  
  Hi Sienna,
  499 is 400 + 4×20 + 19
  so it’s dot, 4 dots, 4 dots over 3 lines
  
  Similarly, 45 is 2×20 + 5
  so it’s 2 dots, 1 line
  
  Reply