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
-1part. As a consequence, the
-1 * -1could be interpreted as apply two consecutive negation, which is identity.