Machinery’s Handbook 28th Edition: MATHEMATICS

TABLE OF CONTENTS

NUMBERS, FRACTIONS, AND DECIMALS

3 Fractional Inch, Decimal, Millimeter Conversion
4 Numbers
4 Positive and Negative Numbers
5 Sequence of Operations
5 Ratio and Proportion
7 Percentage
8 Fractions
8 Common Fractions
8 Reciprocals
9 Addition, Subtraction, Multiplication, Division
10 Decimal Fractions
11 Continued Fractions
12 Conjugate Fractions
13 Using Continued Fraction
14 Powers and Roots
14 Powers of Ten Notation
15 Converting to Power of Ten
15 Multiplication
16 Division
16 Constants Frequently Used in Mathematical Expressions
17 Imaginary and Complex Numbers
18 Factorial
18 Permutations
18 Combinations
19 Prime Numbers and Factors

ALGEBRA AND EQUATIONS
29 Rearrangement of Formulas
30 Principle Algebraic Expressions
31 Solving First Degree Equations
31 Solving Quadratic Equations
32 Factoring a Quadratic Expression
33 Cubic Equations
33 Solving Numerical Equations
34 Series
34 Derivatives and Integrals

GEOMETRY

36 Arithmetical & Geometrical Progression
39 Analytical Geometry
39 Straight Line
42 Coordinate Systems
45 Circle
47 Ellipse
50 Spherical Areas and Volumes
53 Parabola
53 Hyperbola
65 Areas and Volumes
65 The Prismoidal Formula
65 Pappus or Guldinus Rules
66 Area of Revolution Surface
66 Area of Irregular Plane Surface
67 Areas of Cycloidal Curves
67 Contents of Cylindrical Tanks
69 Areas and Dimensions of Figures
75 Formulas for Regular Polygons
76 Circular Segments
79 Circles and Squares of Equal Area
80 Diagonals of Squares & Hexagons
81 Volumes of Solids
87 Circles in Circles and Rectangles
92 Circles within Rectangles
93 Rollers on a Shaft

SOLUTION OF TRIANGLES

94 Functions of Angles
95 Laws of Sines and Cosines
95 Trigonometric Identities
97 Right-angled Triangles
100 Obtuse-angled Triangles
102 Degree-radian Conversion
104 Functions of Angles, Graphic
105 Trig Function Tables
109 Versed Sine and Versed Cosine
109 Sevolute and Involute Functions
110 Involute Functions Tables
114 Spherical Trigonometry
114 Right Spherical Trigonometry
116 Oblique Spherical Trigonometry
118 Compound Angles
120 Interpolation

LOGARITHMS

121 Common Logarithms
122 Inverse Logarithm
123 Natural Logarithms
123 Powers of Number by Logarithms
124 Roots of Number by Logarithms
125 Tables of Logarithms

MATHEMATICS
Machinery’s Handbook 28th Edition

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TELL US…in your own words

Seneca students,

I need you to help us make Seneca even better.

  During the week of April 5-9, you’ll have a chance to tell us how we are doing in the services and activities outside of your classroom. For more information, a video is online at http://www.senecac.on.ca/marketing/tell-us/index.html

Take part in Seneca’s version of Speaker’s Corner or get interviewed as we’ll have members of our team at your campus approaching you for your opinions.

Have your say – in your own words – and make every student’s time at Seneca a great experience.

  Thank you,

David Agnew
President, Seneca College

TELL US…in your own words:

Monday April 5: Jane Campus
Interviews all day
Speaker’s Corner 9 a.m. – 11 a.m., Lobby
 
Monday April 5: Markham Campus
Interviews all day
Speaker’s Corner 12 p.m. – 3 p.m., Cafeteria

  Tuesday April 6: King Campus
Interviews all day
Speaker’s Corner 11 a.m. – 3 p.m., Cafeteria

  Wednesday April 7: Seneca@York Campus
Interviews all day
Speaker’s Corner 11 a.m. – 3 p.m., Cafeteria

  Thursday April 8 and Friday April 9: Newnham Campus
Interviews all day
Speaker’s Corner 11 a.m. – 3 p.m.
April 8 – Senecentre
April 9 – Building B, second floor, next to Learning Commons  

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Pythagorean Theorem: Part 1

Professor R. Smullyan in his book 5000 B.C. and Other Philosophical Fantasies tells of an experiment he ran in one of his geometry classes. He drew a right triangle on the board with squares on the hypotenuse and legs and observed the fact the the square on the hypotenuse had a larger area than either of the other two squares. Then he asked, "Suppose these three squares were made of beaten gold, and you were offered either the one large square or the two small squares. Which would you choose?" Interestingly enough, about half the class opted for the one large square and half for the two small squares. Both groups were equally amazed when told that it would make no difference.

The Pythagorean (or Pythagoras'Theorem is the statement that the sum of (the areas of) the two small squares equals (the area of) the big one.

In algebraic terms, a² + b² = c² where c is the hypotenuse while a and b are the legs of the triangle.

The theorem is of fundamental importance in Euclidean Geometry where it serves as a basis for the definition of distance between two points. It's so basic and well known that, I believe, anyone who took geometry classes in high school couldn't fail to remember it long after other math notions got thoroughly forgotten.

Below is a collection of 82 approaches to proving the theorem. Many of the proofs are accompanied by interactive Java illustrations.

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