If Isaac Newton invented Calculus, then who invented Pre-Calculus?
Why are these two separated? Whose idea was this?
Why are these two separated? Whose idea was this?
2 Answers
I do not think that anybody is attributed with invention of precalculus. Calculus needs many things or prerequisites which may be necessary for some one to understand calculus. Hence Prcalculus was introduced for those interested in pursuing calculus as subject.
A little history...
Explanation:
Sir Isaac Newton, shortly before his death, it reputed to have said:
I don't know what I may seem to the world, but as to myself, I seem to have been only like a boy playing on the sea-shore and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
In ancient times, well before Newton's day, small pebbles were used for counting, especially in abacuses. Such a small pebble was called (in Latin) a "calculus".
When Newton needed some mathematical language in which to develop his ideas about mathematical physics he discovered, developed, formulated or (if you will) invented a collection of methods that today form an essential part of modern calculus:
- Chain rule
- Product rule
- Second and higher derivatives
- Taylor series
- Analytical functions
There are many more parts to calculus that Newton did not develop.
Note that some fundamental parts of calculus pre-date Newton. Also Gottfried Leibniz (who was accused of plagarising Newton) independently discovered some of these ideas at the same time.
Later mathematicians - especially Euler - further developed infinitesimal calculus.
Ideas concerning infinitesimals were around a long time ago, as were ideas about limits (e.g. the geometrical construction called "neusis"). So Newton was not exactly producing his ideas out of thin air. That having been said, he did contribute substantially.
What we call pre-calculus is simply a collection of material to prepare for the study of calculus. It has no particular hero to whom we might (rightly or wrongly) ascribe or blame it.