Pi Archives - The Nature of Mathematics

Reference Topics 18-4

April 25, 2018July 23, 2015 by elaine

This is a more advanced site than we need for the introduction in this book, but check out the following discussion of area under a curve:
https://www.intmath.com/integration/3-area-under-curve.php… See the whole entry

Reference Topics 18-1

May 21, 2024July 23, 2015 by elaine

Zeno’s paradox is discussed at this site:
http://mathforum.org/isaac/problems/zeno1.html

An interesting article on mathematical modeling and why it is important is found at this site:
https://www.skylineuniversity.ac.ae/knowledge-update/from-different-corners/why-is-mathematical-modelling-so-important… See the whole entry

Section 8.1: Perimeter

September 25, 2015July 13, 2015 by elaine

8.1 Outline

Introduction
1. measure
2. precision/accuracy
  1. accuracy procedure used in this book
  2. metric world in 2010
Measuring length
1. define length
  1. U.S. system
  2. metric system
2. standard length units
  1. U.S. system
  2. metric system; prefixes
Perimeter
1. define perimeter
2. formulas
  1. equilateral triangle
  2. rectangle
  3. square
Circumference

… See the whole entry

Reference Topics 5-5

July 23, 2017July 8, 2015 by elaine

A variety of proofs of the Pythagorean theorem are found at this site. There are also some interesting remarks concerning this theorem:
http://www.cut-the-knot.org/pythagoras/index.shtml

For those of you who think that irrational numbers can be written in some (yet unknown) … See the whole entry

The most famous real numbers that are not rational are the numbers pi and e. However there are many interesting constants in mathematics, as described at the following site:
http://sprott.physics.wisc.edu/pickover/trans.html

The number 0, the additive identity, is the subject … See the whole entry

Section 5.6: Groups, Fields, and Real Numbers

September 24, 2015July 8, 2015 by elaine

5.6 Outline

Definition of real numbers
1. definition
2. decimal representation
  1. terminating decimal
  2. repeating decimal
  3. change fractional form to decimal form
  4. change terminating decimal form to fractional form
3. real number line
  1. unit distance
  2. number line
  3. dense set
4. classifications within the set of

… See the whole entry