"Mathematics is the Queen of Science, and Arithmetic the Queen of Mathematics" -- (Carl Friedrich Gauss, 1777-1855)
Aristotle (c. 350 B.C.): A student of Plato, Aristotle was more of a physicist than a mathematician, but he promoted deductive logic in his writing on physical subjects. He was a thinker, and he definitely saw mathematics as a human activity. Aristotle was a humanist, and he criticized all forms of government, especially the two competing in Athens during his time - democracy and oligarchy.
What does Herkimer call a lawyer who is hired by a person who smashed his car into the back of another car?
Answer: A rear-ender fender bender defender.
WALTER WALL...a carpet installer.
HARRY FITABALDI ... president of a wig-making company.
Reading: Section 1.5, pages 33-37.
Written: Page 38/18-23.
Mathematical word analysis:
EXPONENT: From the union of the Latin words exo (out of) and ponere (place). When you write 35, the 5 is, in a manner of speaking, "out of place." We know that 35 = 3x3x3x3x3 = 243. Since the 5 is "out of place," we don't interpret the number 35 to be 35.
Very seldom in life does one simply come across equations that need to be solved. In a more likely situation, one is presented with a verbally-stated problem. The task is to "translate" the the problem into an algebraic setting so it can be solved.
When doing the translation, it is important to define clearly all variables that you introduce. Here is an example:
Herkimer has $2,400 invested, part of it at 5%, and the remainder at 8%. If he receives $132 in interest, what amounts are invested at each rate?
Let x = amount (dollars) invested at 5%.
Then 2400 - x = amount (dollars) invested at 8%.
Premise ==> .05x + .08(2400 - x) = 132
==> .05x + 192 - .08x = 132
==> .03x = 60
==> x = 60/.03 = 2000 (dollars).
Conclusion: Herkimer has $2,000 invested at 5% and $400 invested at 8%.
Note that the variable x is clearly defined, a reader could follow the solution process, and the desired answer is clearly indicated.
Practice being neat when you solve mathematical problems. This will enhance your appreciation of the power of mathematics.
Problem constructed by American poet and scholar Henry Wadsworth Longfellow (1807-1882):
One-third of a collection of beautiful water lilies is offered to Mahadev, one-fifth to Huri, one-sixth to the Sun, one-fourth to Devi, and six which remain are presented to the spiritual teacher. Find the number of water lilies.
Solution (with communication):
Let x = the number of water lilies in the collection. Then the premise implies
(1/3)x + (1/5)x + (1/6)x + (1/4)x + 6 = x
==> 60[(1/3)x + (1/5)x + (1/6)x + (1/4)x + 6] = 60x
==> 20x + 12x + 10x + 15x + 360 = 60x
==> 57x + 360 = 60x
==> 3x = 360
==> x = 120.
The original collection contained 120 water lilies.