“Three”: Tripod, Three Sides make a Triangle
“Three” 查看中文： “3” 三人成众
Three sounds pretty close to “tree”, there are lots of trees in a forest.
Have you heard the word “tripod”? Here “tri-” means three.
> The minimal property for number 3: a polygon has at least 3 sides, the smallest odd prime is 3. The first and the smallest triangle number is also 3 (number 3 = 1 + 2).
If not counting “1”, then number 3 is the smallest odd number.
Oddly enough, “3” also means “many” in some cultures.
> All integers are divided into 3 categories: positive integers, zero, and negative integers.
> 32 = 3 X 3 = 9, 23 = 2 X 2 X 2 = 8; 9 and 8 are the largest and the second largest digits in the decimal (base-10) system.
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To test whether a number is divisible by 3 (has factor 3), it is enough to add all the digits of the number, and check weather the sum of digits has factor 3.
Example: 15 [1+5=6], 6 has factor 3, so 15 is divisible by 3.
121 (1+2+1=4), 4 does not contain factor 3, therefore 121 is not divisible by 3.
> The sum of any three consecutive integers is divisible by 3.
> The 3-4-5 triangle is the smallest right triangle with all three integer side lengths.
This fact is also interesting: if a right triangle has three sides of integer lengths, then at least one side length is a multiple of 3.
Examples: we list some right triangles with integer side lengths:
3-4-5, 5-12-13, 8-15-17, 7-24-25,
in which 3, 12, 15, 24, .. are the multiples of 3.
> When we say the most, we mean a fraction of total: the fraction may be (2/3) (two-thirds) or (3/4) (three quarters).
