Art ignites the imagination, and one of the fascinating aspects of art is the use of patterns.
Pascal's Triangle shows many patterns that are useful in mathematics. The third diagonal from the left shows the triangular numbers (3, 6, 10, 15...) These numbers show the number of dots that are needed in order to create a triangular shape.
Another pattern that can be seen with triangular numbers is when adding the counting numbers together.
(1+2= 3, 1+2+3= 6, 1+2+3+4= 10, and 1+2+3+4+5=15,...)
When adding together a the numbers 1-10 in the same way a pattern can be found.
For example the sum of the numbers 1-10 is the tenth triangular number on the pyramid above. What patterns do you notice in the numbers leading up to the triangular number 10?
Here's a hint: if you take the 2nd triangular number 6, and compare it to the ones in front of it and behind it, what do you notice?
Another clue is if you list the addends and add the first and last numbers, what do you notice?
Mathematicians notice patterns and experiment with writing equations to show a general rule. These patterns can create pyramid's of numbers that continue to grow.
