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 longhaunting 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 “multiduty” 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 the1
part. As a consequence, the1 * 1
could be interpreted as apply two consecutive negation, which is identity.