# Intuition goes a long way

Came across Better Explained the other day, and was really amazed by the intuitive explanation from the author.

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List of surprising points struck me while reading:

The sum formula for arithmetic series could be understood as

`mean * number`

.Didn’t know there’s dedicated name, “Fencepost Problem”, for this long-haunting problem since I was a kid. If the structure is one loop, then the number of spans is the same as the number of points. If the points are used in a “multi-duty” manner, then

`#spans > #points`

. One vivid example could be the global, with two poles being the points, and lines of longitude being the spans.The explanation on the multiplication of two negative numbers is a positive number is not very clear to me. I feel a much better way of constructing the reasoning could be destruct negative number in multiplication into

`-1 * <positive number>`

, then use repeatable addition for the`<positive number>`

part, and negate for the`-1`

part. As a consequence, the`-1 * -1`

could be interpreted as apply two consecutive negation, which is identity.