“Two” – In Pairs
“Two”
Whether you like it or not, number “2” is fairly important in math.
> Any number that can be divisible by 2 (has a factor of 2) is called an even number. Otherwise it is an odd number.
> 2 is the smallest prime number. (A prime number is a natural number that cannot be written as the product of even smaller numbers).
2 has two divisors: 1 and 2. Any prime number has two divisors.
> Look at the identity.
x + x = 2x, (x) (x) = x2
where x2 is read as “x square”.
Conclusion: we meet number “2” quite often in both arithmetic and algebra.
> 2 is the base for binary system (Carry one to next higher place whenever we reach two). The numbers in a binary system are 0, 1, 10, 11, 100, 101, … .
> The numbers in power of 2, when written in decimal system (the usual system) are:
（1），2，4，8，16， …
In such a sequence, the sum of consecutive items starting from 1 is always one less than the next item, e.g., 1 = 2-1， 1+2 = 4-1， 1+2+4 = 8 -1，etc.
> Look at this equation on the sum:
1 + 1/2 + 1/(22) + 1/(23) + … = 2
Conclusion: what would you say? _______________
> (Algebric) Squares are the powers when the exponent is 2. We calculate the area of a square shape by squaring side of that shape.
From Pythagorean Theorem: in a right triangle, the sum of squares of the two sides equals the square of the length of hypotenuse.
> The binomial power (a+b)n is studied in early classic algebra and is a classic topic in high school algebra. (We do not have 2 here, however, a and b are two items).
Expansion this into polynomial, one tool is Pascal triangles. [This entry is a bit deeper.]
> When thinking of “two”, think of being in pairs, and think of even and odd!
