Jan 22, 2010

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See also Essays in Mathematics, Other Recommended Math Sites,
and selected answers to common questions.

Frequently  Asked  Questions

Classic Problems
Age Word Problems; Birthday Probability
Boy or Girl?; Camel and Bananas
Coin Problems; Doubling Pennies; Grazing Animals
Liars and Truthtellers; Missing Dollar
Monty Hall; Three Houses-Three Utilities
Tower of Hanoi; Two Trains; Two Trains & Fly

0.9999... = 1
Why does 0.9999... = 1?

0 to 0 power
What is 0 to the 0 power?

n to 0 power
Why is any number raised to the zero power equal to one?

0! = 1
Why does 0! = 1?

Calendar & Days of the Week
What years are leap years? How do I find the day of the week for any date? How do I find a calendar for any year? How common are Friday the 13ths?

Cubic and quartic equations
What are the general solutions to cubic and quartic polynomial equations?

Distance, Rate, and Time
Distance = Rate x Time: A discussion and two problems.

Dividing by 0
Why can't you divide by 0? Why is 0/0 "indeterminate" and 1/0 "undefined"? Why is dividing by zero "illegal"?

Dividing Fractions
How do you divide fractions? Say, 2/3 divided by 3/4.

Divisibility rules
How can you tell whether a number is divisible by another number (leaving no remainder) without actually doing the division? Why do 'divisibility rules' work?

E = 2.71828...
What is e? Who first used e? How do you find e? How many digits does it have?

False Proofs, Classic Fallacies
What's wrong with proofs that say 1+1=1, or 2=1?

Fermat's Last Theorem
What is the current status of Fermat's Last Theorem?

Fractions, Decimals, Percentages
What are simple, complex, and compound fractions? How do you convert decimals and percentages to fractions?

Golden Ratio, Fibonacci Sequence
Please tell me about the Golden Ratio (or Golden Mean), the Golden Rectangle, and the Fibonacci Sequence.

Imaginary numbers
What is an imaginary number? What is i? And see Imaginary Exponents and Euler's Equation.

Impossible constructions
Problems from antiquity: trisecting an angle, squaring the circle, duplicating the cube.

Integers, Rational/Irrational Numbers
What is an integer? Are fractions rational numbers? What about .9999...? How about decimals? pi? the Golden Ratio?

Large numbers and infinity
What's the largest number? What's a googol? How do we name large numbers? What is infinity?

Learning to factor
A sampling of answers from our archives.

Loans and Interest
Interest calculations: simple interest, compound interest, annual percentage rate (APR), installment loans.

Math terms
Why was the letter m selected to represent slope? What's the name of the "fraction bar"?

Multiplication facts
Tips for parents, teachers, and students for different ways of learning to multiply. In particular, see Russian Peasant Multiplication.

Naming polygons and polyhedra
What do you call an 11-sided polygon? A 14-sided polygon? Is there a list of names of polygons?
Formulas, by Robert L. Ward
Defining Geometric Figures; Geometric Formulas
Analytic Geometry Formulas
  Polar Coordinates
  Spherical Coordinates
  Cylindrical Coordinates)
Trigonometry Formulas

Negative times a negative
Why does a negative times a negative equal a positive? Does this ever happen in the real world?

Number bases
What is base 10? Binary? Hexadecimal? How can you convert from one base to another?

Number glossary
What are abundant, amicable, deficient, figurate, happy, narcissistic, palindromic, perfect, polygonal, proper divisors, semiperfect, sociable, square, tetrahedral, triangular, and weird numbers?

Order of operations
What is the correct order of operations? Why use it? What is PEMDAS?

Pascal's triangle
What is Pascal's Triangle? How do you construct it? What is it good for?

Perfect numbers
What is a perfect number? How many are there? How can you calculate a perfect number from a Mersenne prime?

Permutations and Combinations
How to calculate all the groupings of objects where order does or doesn't matter. And see Fast Food Combinations.

Pi = 3.14159...
What is Pi? Who first used Pi? How do you find it? How many digits is it?

Prime numbers
What is a prime number? What's the 'Sieve of Eratosthenes'? What is the largest known prime?

An introduction to basic concepts. See also Probability in the Real World.

What is a proof? How do you write a two-column proof?

Properties Glossary
What is an operation? an identity? What are the associative, commutative, distributive, and equality properties? What is the property of closure? What is the inverse of something?

Pythagorean theorem
What is the Pythagorean theorem? When would I use it?

Pythagorean triples
What are Pythagorean triples? What do they have to do with Fermat's Last Theorem?

Roman Numerals
How to read and write Roman numerals; Roman numeral fractions; arithmetic problems; and resources for other numeral systems.

Rounding Numbers
How do you round a number to the nearest 10th, 100th, 1000th, etc.?

Segments of circles
Given partial information about a segment of a circle, how do you compute what you want to know?

Square/cube roots without a calculator
How do you find the square root of a number by hand? How about cube roots?

Trachtenberg speed system
Doing high-speed basic operations in your head.

Typing math
How should I type exponents? What about square roots? Why not use tabs? May I send attachments?

Why study math? How to study math
Why do we need to learn math? When are we ever going to use it in real life? Math study tips.

Word Problems
When I'm given a 'word problem', where do I start?

Working Together
Jack can finish a job in 5 days, and Richard can finish the same job in 7 days. Working together, how long will it take them to finish the job?

Essays in Mathematics by our Math Doctors

A Crash Course in Symbolic Logic - D. J. Brasier (Dr. Achilles)
An introduction to the notation and rules of derivation in symbolic logic.

Nonstandard Analysis and the Hyperreals - Jordi Gutierrez Hermoso (Dr. Jordi)
An introduction to the most basic ideas of nonstandard analysis and the hyperreal number system.

Other Recommended Math Sites

Math History

Earliest Uses of Mathematical Symbols and
Earliest Uses of Some Words of Mathematics - regularly updated by Jeff Miller.

Famous Problems in Math History
by Isaac Reed, Swarthmore College

History of Mathematics
by David Joyce, Clark University

MacTutor Math History Archive - St. Andrews
A searchable archive of articles and biographies

Mathematicians of the African Diaspora
Ancient and modern history, by Dr. Scott W. Williams

Women Mathematicians
Biographies by students from Agnes Scott College

Unit Conversion

How Many?
A Dictionary of Units of Measurement by Russ Rowlett, Univ. of North Carolina at Chapel Hill.

ConvertIt.com Measurement Converter
Entisoft's comprehensive converter for distance, area, volume, mass, speed, temperature, pressure, energy, power, force, etc.- over 500 different unit conversions.

OnlineUnitConversion.com Measurement Converter
Another extensive converter for acceleration, angles, area, currency, energy, force, power, pressure, speed, and more.

To convert temperature, length, weight, and volume see the Unit Conversion Program or the megaConverter.

Metric System and Anglo-Saxon Units
Weights and measures: history and correlations,
by Jacques J. Proot

Math Reference

Eric Weisstein's World of Mathematics
Definitions and examples.

Euclid's Elements
All 13 books, with interactive illustrations.

Forum Internet Mathematics Library
Search for Math on the Internet.

Flash Cards for Kids
Addition, subtraction, multiplication, division; three levels of complexity and numbers from 1 to 999.

Free On-Line Dictionary of Computing (FOLDOC)
A searchable dictionary of anything to do with computing. Includes a section on mathematics.

Glossary of Statistical Terms
Basic definitions and much more.

Mathematics Glossary for Middle-Level Students
Simple definitions of math terms.

Mathematical Quotation Server
A collection of quotations from many sources.

Math Words, and Some Other Words, of Interest
Pat Ballew's list of over 450 mostly math words, their definitions, and etymologies.

On-Line Encyclopedia of Integer Sequences
Look up a sequence, word, or sequence number. Maintained by N. J. A. Sloane.

Plouffe's Inverter
A database of mathematical constants.

Type your Algebra 1 problem directly into this site and get a step-by-step solution.

Submit your own question to Dr. Math

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