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.