What's a number ? - Interactive Mathematics Miscellany and PuzzlesA number r is rational if it can be written as a fraction r = p/q where both p and q
are integers. In reality every number can be written in many different ways. To be
...

Binary puzzle - Interactive Mathematics Miscellany and PuzzlesIn the Boolean Algebra , one normally defines conjunction (&, AND), ... The
purpose of the game is to get all 16 squares filled with the right numbers which
are ...

Fast Arithmetic Tips - Interactive Mathematics Miscellany and PuzzlesFast Arithmetic Tips, how to speed up calculations. ... E. H. Julius, More Rapid
Math Tricks And Tips, John Wiley & Sons, 1992; S. Flansburg, Math Magic,
William ...

Stunning Friends With Math MagicA collection of card tricks , number guessing games, paper and glue magic , and
other math exercises. A Baffling Prediction - A Matter of Age - An Arithmetic Magic Trick - Magic in a Square

What Is Trigonometry ?Trigonometry defines relations between elements of a triangle. In a triangle, there
are six basic elements: 3 sides and 3 angles. Not any three line segments may ...

Fast Arithmetic Tips: Getting the Result FastFast Arithmetic Tips, how to speed up calculations . It's often more convenient
instead of multiplying by 5 to multiply first by 10 and then divide by 2, etc...

Equivalence RelationshipThe last one enables me to point out how omnipresent equivalence relations
actually are. People invent symbols (known as words) to denote some objects.

A number r is rational if it can be written as a fraction r = p/q where both p and q
are integers. In reality every number can be written in many different ways. To be
... rational and irrational - real and complex - imaginary - algebraic and transcendental

Adding a Long List of NumbersFor some people, adding a list of not very different numbers is a frequent task. To
me this happens every time I feel my tax returns; there is always a few dozen ...

Matrices Help RelationshipsMatrices Help Relationships . Once when I was a graduate student I had a
conversation with a philosophy professor friend about epistomology. He said
there is a ...

What Is Point ? - Interactive Mathematics Miscellany and PuzzlesPoint is a basic concept of elementary geometry. The idea of point is an
abstraction that distils our understanding of the concept of location.

Fast Arithmetic Tips. Mental Calculations - Getting the result fast. Addition of 5.
When adding 5 to a digit greater than 5, it is easier to first subtract 5 and then add
...

Squaring the Circle - Interactive Mathematics Miscellany and PuzzlesSquaring the Circle : it is impossible to construct a square equal in area to a given
circle with compass and straightedge.

Sieve of Eratosthenes - Interactive Mathematics Miscellany and Sieve of Eratosthenes : an ancient way of getting the prime numbers.
Eratosthenes (276-194 B.C.) was the third librarian of the famous library in
Alexandria and ...

Eight Digits Puzzle - Interactive Mathematics Miscellany and PuzzlesPlace eight digits 1 through 8 into eight circles , but there is a caveat. ... The
diagram can of course be looked at as a graph whereas the digits are being
assigned ...

The Three Jugs Problem . Introduction and a storyowed his interest in mathematics to a chance encounter with a simple problem :
Two friends who have an eight-quart jug of water wish to share it evenly.

Equations of a Straight LineEquations of a Straight Line : a line through two points, through a point with a
given slope, a line with two given intercepts, etc.

Mathematical Induction - Interactive Mathematics Miscellany and Mathematical Induction . Definitions and examples of induction in real
mathematical world.

Tower of Hanoi - Interactive Mathematics Miscellany and PuzzlesThe Tower of Hanoi puzzle was invented by the French mathematician Edouard
Lucas in 1883. We are given a tower of eight disks (initially four in the applet ...

Random Walks - Interactive Mathematics Miscellany and PuzzlesRandom Walks . A random walk is a formalization of a discrete process wherein a
random selection is made between two alternatives (often ~+mn~1) at fixed ...

Did you know that ... Random interesting math facts, part 1. ... Everything you can do with a ruler and a compass
you can do with the compass alone; Among all shapes with the same perimeter ...

Monty Hall Dilemma - Interactive Mathematics Miscellany and PuzzlesSuppose you're on a game show, and you're given the choice of three doors .
Behind one door is a car, behind the others, goats. You pick a door , say number
1 , ...

Example: A Poker HandPoker uses the standard deck of 52 cards. ... The highest ranking poker hand is a
Royal Flush - a sequence of cards of the same suit starting with 10, e.g., ...

Parabolic Mirror , TheoryParabolic Mirror : the tangent to parabola at a point bisects the angle between the
segments joining the point to the focus and the directrix.

Implementation of Base Conversion Algorithms from Interactive Base conversion algorithm: interactive implementation in different bases,binary-
octal-hexadecimal conversion.

What Is Geometry ? - Interactive Mathematics Miscellany and PuzzlesGeometry is perhaps the most elementary of the sciences that enable man, by
purely intellectual processes, to make predictions (based on observation) about ...

What Is Infinity ? - Interactive Mathematics Miscellany and Puzzlesquestions a curious student may ask a math teacher is whether 1/0 is infinity or
not. And then of course comes another thoughtful extension: Is 1/ infinity = 0?

9 Dots Problem - Interactive Mathematics Miscellany and PuzzlesThe 9 Dots Problem: try to lift some implicitly imposed constraints. ... One
classical example is where nine dots are arranged on the sides and the center of
a ...

Less than, Equal to, Greater Than Symbols from Interactive The symbol of equality is used to make a statement that the two differently looking
expressions are in fact equal . For example, 1 + 1 does not look like 2 but the ...

Deleting Pages - Interactive Mathematics Miscellany and PuzzlesTo delete a page , edit the page , select (highlight) all text in the edit textarea and
... This page may have a more recent version on pmwiki .org: ...

Less than , Equal to, Greater Than Symbols from Interactive The symbol of equality is used to make a statement that the two differently looking
expressions are in fact equal. For example, 1 + 1 does not look like 2 but the ...

Interactive Mathematics Miscellany and PuzzlesAn encyclopedic collection of math resources for all grades. Arithmetic games,
problems, puzzles , and articles.

Modular arithmetic, examples, applications2222 5555 + 5555 2222 = 3 5555 + 4 2222 ( mod 7 ). There are only 7 residue
classes modulo 7 . Therefore, the series of powers of a given number ( modulo 7 )
is ...

Hausdorff Distance - Interactive Mathematics Miscellany and PuzzlesHausdorff Distance . We talk about points in a space, like in the definition of a
circle as a set of all points equidistant from a given point. But we have already ...

100 Prisoners and a Light BulbEach of n prisoners will be sent alone into a certain room, infinitely often, but in ...
one prisoner will turn on the light, and no prisoner turns it on more than once.

Mirror Maze - Interactive Mathematics Miscellany and PuzzlesMirror Maze : navigate a maze of mirrors to cover all available cells in a square
grid. ... Home · Wiki ; Subjects. What is What · Algebra · Arithmetic · Geometry ...

Is Mathematics Beautiful?Mathematics , as much as music or any other art , is one of the means by which we
rise to a complete self-consciousness. The significance of Mathematics resides ...

GCD (M, N) x LCM (M, N) = M x N - Interactive Mathematics GCD (M, N) × LCM (M, N) = M × N. A graphical illustration of the fact that the
product of two integers equals the product of their gcd and lcm .

Proofs in MathematicsProofs , the essence of Mathematics - beautiful proofs , simple proofs , engaging
facts. Proofs are to mathematics what spelling (or even calligraphy) is to poetry.

What do you call a centipede?This fellow has only 30 to 40 legs and a relatively short body. In a strange kind of
a way it's classified as related more to the millipedes than to the centipedes.

Mathematics as a LanguageMathematics as a language . Expressing things differently. Blake wrote: I have
heard many People say, 'Give me the Ideas. It is no matter what Words you put ...

What Is Algorithm ? - Interactive Mathematics Miscellany and PuzzlesSimple as the definition of the notion of algorithm is, the concept of what it
attempts to convey is a matter of debate and scientific research.

What Is Algebra ? - Interactive Mathematics Miscellany and PuzzlesBut when we come to the end of our arithmetic we do not content ourselves with
guesses; we proceed to algebra -- that is to say, to dealing logically with the fact ...

Block ' N Roll - Interactive Mathematics Miscellany and PuzzlesBlock ' N Roll : a devilish puzzle. Roll a 2x1x1 block over available squares and
seeze it into a whole. Do not fall over the edge!

Box Labels - Interactive Mathematics Miscellany and PuzzlesIn the applet, select box . One of the two balls it contains will pop up. After which
you'll have to drag labels (they will appear at the right moment) into the empty ...

The Nature of PiThe Nature of Pi : objects have shape and size. Objects of the same shape are
similar. Existence of Pi follows from the fact that all circles have the same shape.

CTK Wiki Math - PmWiki - FAQPmWiki is a wiki-based system for collaborative creation and maintenance ...... Is
there a way that people could self- register through AuthUser ?

Block 'N Roll - Interactive Mathematics Miscellany and PuzzlesBlock 'N Roll : a devilish puzzle. Roll a 2x1x1 block over available squares and
seeze it into a whole. Do not fall over the edge!

Number Guessing Game . All by ComputerNumber Guessing Game , an example of usefulness of the binary system.
Computer does ... In this simple game , your computer does all the work. You only
have ...

Other sites - Interactive Mathematics Miscellany and PuzzlesRecommended math sites . A very exclusive collection of links of exceptionally
worthy sites .

Proofs are to mathematics what spelling (or even calligraphy) is to poetry.
Mathematical works do consist of proofs , just as poems do consist of characters.

Cartesian Coordinate System : an interactive tool, definitions and examples. ... A
straight line with an associated direction, a selected point and a unit length is ...

Sam Loyd's Geometric PuzzleI've been thumbing through Mathematical Puzzles of Sam Loyd selected and
edited by Martin Gardner (Dover, 1959), when I came across a puzzle whose set
...

Interactive Mathematics Activities for Arithmetic, Geometry, Algebra, Probability, ...
and the Least Common Multiple · Compare Fractions: Interactive Practice ...

Stunning Friends With Math Magic · Divisibility Criteria ... A. Benjamin and M.
Shermer, Secrets of Mental Math , Three Rivers Press, 2006. ... Movie shortcuts

The Constitution and Paradoxes. In another demonstration of the Alabama paradox, for all sizes
between 350 and 400, but 357, the state of Colorado would get three seats, with
...

Sample Spaces and Random VariablesA random variable is a function defined on a sample space . We shall consider
several examples shortly. Later on we shall introduce probability functions on the
...

Hummer's Mind ReaderThe computer is going to read your mind and announce which one you've been
thinking .... Mind Reader from Interactive Mathematics Miscellany and Puzzles .

Bayes ' Theorem - Interactive Mathematics Miscellany and PuzzlesBayes ' Theorem : definitions and non-trivial examples . ... Bayes ' Theorem . Bayes '
theorem (or Bayes' Law and sometimes Bayes' Rule) is a direct application of ...

Bulls and Cows - Interactive Mathematics Miscellany and PuzzlesBulls and Cows : a mastermid variant where one has to guess the values of the
hidden digits. But where are the bulls? And which ones are the cows? I do not ...

A Stack of Fake CoinsThere are 10 stacks of 10 identical-looking coins . All of the coins in one of these
stacks are counterfeit, and all the coins in the other stacks are genuine.

Less than, Equal to, Greater Than Symbols . If A and B are two constant
expressions, we write A = B if they are equal, and A ≠ B, if they are not. For
example, for ...

A Mathematical Rabbit out of an Algebraic HatThe proof depends on the following identity that holds for non-negative x, y, z: (2).
x³ + y³ + z³ - 3xyz = ½(x + y + z)(( x - y ) ² + (y - z)² + (z - x)²). which is just another ...

Hypocycloids - Interactive Mathematics Miscellany and Puzzles>Here I wish to consider a special case of hypocycloids where the radius r of the
rolling circle k is exactly half that of the fixed circle K, ... Home · Wiki ; Subjects.