About Foundation of
Math
The science of
number and the science of form are called – mathematics. The science of number
is covered by arithmetic and its big children, algebra and calculus. The
science of form (triangles, circles, cubes, and such) is covered by geometry, and
all its offspring.
Zero is the Father of Mathematics
The introduction
of the symbol “o” is the greatest step ever taken in the history of arithmetical
science, and one that completely escaped the Greeks and Romans. The zero was surely
a happy thought. It passed from the Hindus of India to the Arabs of Arabia, Egypt,
and Coney Island. The figures we now use came in the same package from the same
people. These figures took the place after awhile of the letters used by the ancients,
I, V, X, L, for example. Our present figures, however, are deformed descendents
of letters.
It was the zero
(which means empty space) that brought about in some way the idea that a figure
represents ten times as much in any place as in the succeeding place. That is,
the zero gave birth to the position system in number.
The old Hindu (the
great mathematician Aryabhatt) who first thought of this scale of ten (units,
tens, hundreds, thousands, tens of thousands, etc.) got his notion probably
from Nature's own counting machine – the ten fingers of man.
Columbus came around
us, somewhere, in 1492. Well, in 1478 the first arithmetic came out. Four years
later another arithmetic appeared. These pioneer books explained the use of the
zero system. They caused the shape of the figures to be accepted as fixtures,
and thus put a stop to the changes in their shape that had been going on.
Basic Difference Between Arithmetic, Algebra and Calculus
A
B C of arithmetic, algebra, and calculus, is something like this: Say the side
of a square is two inches, then the square itself is 2x2 = 4 inches. So we
express this fact in arithmetic thus:
4=22
In
algebra we may use the letters a and b instead of the figures 4 and 2, thus:
A=b2
In
arithmetic, you see, we are dealing with a ‘specific’ square and no
other. In algebra we are dealing with a square of ‘any’ size; that is, with
all squares.
Now
in calculus they say the size of the square ‘depends on’ the length of
its side. That is, the square increases or diminishes as the side changes in
length. That is, the square increases or diminishes as the side changes in
length. You may say that this is an absurdly simple principle. So it is, but it
is a very powerful idea in mathematics, just as that other simple thing,
gravity, is powerful in physics. So we will now take x and y instead of a and b
or 4 and 2, and say the size of x depends on the size of y, or in technical
language, x is a "function" of y. The way that notion is expressed in
calculus is:
x = f(y)
You need not
bother your head about why this artifice is more powerful in problems than
arithmetic or algebra, because it is not used except in complex questions, such
as finding out how things change, or rather at what rate they change.
Thus, roughly speaking,
in arithmetic we have known quantities, in algebra unknown
quantities, in calculus changing quantities.
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