Alpha: Computational Knowledge Engine. Web Equation. Dave's short course in trigonometry. Table of Contents Who should take this course?
Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Math Fun Facts! Contents, Interactive Mathematics Miscellany and Puzzles.
Since May 6, 1997You are visitor number E66B7E in base 20 Raymond Smullyan, a Mathematician, Philosopher and author of several outstanding books of logical puzzles, tells, in one of his books, a revealing story.
A friend invited him for dinner. He told Smullyan that his teenage son was crazy about Smullyan's books and could not wait to meet him. Mathematics Department - General Math Sites. Most Popular Math Fun Facts. History Topics Index. Phi, 1.618, the Golden Ratio and Fibonacci series in life, art, design, beauty, mathematics, geometry, stock markets, theology, cosmology and more. MathPuzzle.com. Elements of Abstract and Linear Algebra by Edwin H. Connell. History Topics. Foundations of Mathematics. Rotor. Banach-Tarski Paradox. Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using rigid motions only, form TWO solid balls, EACH THE SAME SIZE AND SHAPE as the original?
This theorem is known as the Banach-Tarski paradox. So why can't you do this in real life, say, with a block of gold? If matter were infinitely divisible (which it is not) then it might be possible. But the pieces involved are so "jagged" and exotic that they do not have a well-defined notion of volume, or measure, associated to them. In fact, what the Banach-Tarski paradox shows is that no matter how you try to define "volume" so that it corresponds with our usual definition for nice sets, there will always be "bad" sets for which it is impossible to define a "volume"!
Presentation Suggestions: Students will find this Fun Fact hard to believe. The Math Behind the Fact: First of all, if we didn't restrict ourselves to rigid motions, this paradox would be more believable. Pauls Online Math Notes. MathPages. Inspiration gallery. Wolfram MathWorld: The Web's Most Extensive Mathematics Resource. Mathematical Atlas: A gateway to Mathematics. Welcome!
This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) Questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages"). To reach the best page for your interests, use whichever of these navigation tools ("purple pages") you prefer: Nerd Paradise : Divisibility Rules for Arbitrary Divisors. It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number.
Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0. The number is both divisible by 2 and divisible by 3. Cut the number into 2 parts: the last digit and everything else before that. The Fibonacci sequence. Maths Software. Mathematical Definitions of Phi - The Myth of the Golden Ratio. The Mathematical Definitions of PhiLet's start with a working definition of our number.
Phi is defined as the positive, irrational solution to the quadratic equation x^2-x-1=0. If we apply the Quadratic Formula to solve this, we get: The Quadratic Definition of Phi Remember, we're only interested in the POSITIVE solution ((1+sqrt(5))/2). The negative solution is not nearly as interesting as our friend phi. Math Motorway Problem: Connect the towns solution. Triangle Dissection Paradox. PatrickJMT. MathAppendices. NumberSpiral.com - Home. How Mathematics Can Make Smart People Dumb - Ben O'Neill.
Mathematics can sometimes make smart people dumb.
Let me explain what I mean by this. I don't mean that it is dumb not to be good at mathematics. After all, mathematics is a highly abstract and challenging discipline requiring many years (decades even) of study, and there are plenty of very smart people who have little understanding of it, and little ability to use it. What I mean is that mathematics quite often bamboozles people into accepting very silly arguments — arguments that are so silly that if you stated them without draping them in mathematical negligee, you would instantly become an object of ridicule to all those people who flunked out at basic algebra back in high school.
The danger of mathematical arguments is that a person can sometimes follow an absurd path of reasoning without being alerted to its absurdity, due to the fact that their mind is so lost in the verbiage of mathematical equations that their common sense fails to penetrate it. But wait a minute. Notes. Mathpi. Hammack Home. This book is an introduction to the standard methods of proving mathematical theorems.
It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) The two editions can be used interchangeably, except for the last few pages of Chapter 13.
Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. How to construct (draw) the incircle of a triangle with compass and straightedge or ruler.