I like 'Better Explained'[1]. It specifically focuses on intuitive understanding of mathematics.
A post I like is on adding numbers 1 to 100 [2]. The staple formula is n(n+1)/2, sum of arithmetic progression. How can we intuitively arrive that this formula?
> Technique 1: Pair Numbers
Pairing numbers is a common approach to this problem. Instead of writing all the numbers in a single column, let’s wrap the numbers around, like this:
1 2 3 4 5
10 9 8 7 6
An interesting pattern emerges: the sum of each column is 11. As the top row increases, the bottom row decreases, so the sum stays the same.
Because 1 is paired with 10 (our n), we can say that each column has (n+1). And how many pairs do we have? Well, we have 2 equal rows, we must have n/2 pairs.
Number of Paris x Sum of Each Pair = (n/2) (n + 1) = n(n+1) / 2
A post I like is on adding numbers 1 to 100 [2]. The staple formula is n(n+1)/2, sum of arithmetic progression. How can we intuitively arrive that this formula?
> Technique 1: Pair Numbers Pairing numbers is a common approach to this problem. Instead of writing all the numbers in a single column, let’s wrap the numbers around, like this:
1 2 3 4 5
10 9 8 7 6
An interesting pattern emerges: the sum of each column is 11. As the top row increases, the bottom row decreases, so the sum stays the same.
Because 1 is paired with 10 (our n), we can say that each column has (n+1). And how many pairs do we have? Well, we have 2 equal rows, we must have n/2 pairs.
Number of Paris x Sum of Each Pair = (n/2) (n + 1) = n(n+1) / 2
[1] https://betterexplained.com/
[2] https://betterexplained.com/articles/techniques-for-adding-t...