Ask Dr. Math

High School Archive

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Galley or Scratch Method of Division [12/08/2002]

In the 15th century, what was the method for performing division?

Gallons and Cubic Inches [09/04/2001]

I know that 1 gallon is 231 cubic inches, based on the old English "wine gallon" unit. Why was the number 231 used?

Garfield's Pythagorean Theorem Proof [02/27/1997]

Which President of the United States wrote a proof of the Pythagorean Theorem? On what did he base his proof?

Geometry History [8/8/1996]

I'm looking information about the history of Geometry.

Golden Rectangle History [9/7/1996]

What is the history of the golden rectangle? When was it discovered and by whom?

Halving and Halving Again - Zeno's Paradox [8/22/1996]

Since we can never really get to zero by reducing something by halves, does that mean that we are floating on air?

Harmonic Mean [12/15/1996]

What is the harmonic mean and how do you use it?

Hebrew Mathematics [09/21/2000]

I need to write a one-page article on the Hebrew mathematics system.

History and Applications of the Natural Logarithm [03/02/1998]

I'm so surprised at how often the number e comes up. Where did it come from? Who first derived it? Why is it so common in the field of biology?

History and Discovery of Imaginary Numbers [02/28/2006]

How do mathematicians decide to create something like imaginary numbers and the square root of -1 being (i)?

History and Origination of the Metric System [08/13/2005]

Who invented the metric system?

History of Calculating Pi [05/20/1998]

How have the formulas for pi evolved throughout mathematical history?

History of Circle Area Formula [03/19/2007]

Do we know who figured out that pi*r^2 gives the area of a circle?

History of Complex Numbers [12/12/2005]

Why were complex numbers invented?

History of DeMoivre's Theorem [11/14/1997]

What is the history behind DeMoivre's theorem - did he base it on the work of predecessors?

History of Exponent Notation [11/03/2003]

Why is the symbol for exponents a smaller number above the base? How did it become this? What is the history of it?

History of Imaginary Numbers [03/09/2001]

Who invented imaginary numbers?

The History of Numbers and Numerals [12/08/1998]

Can you give me some information on the history of numbers? How were they developed and where are they used?

History of Numerals and Counting: Bibliography [11/18/1996]

Where do I find information on different systems of measurements?

History of Numerals and Symbols [06/22/1998]

Why and when did the change from Roman to Hindo-Arabic numerals occur? What is the history of +, -, =, /, etc.?

History of Odd and Even Numbers [02/12/2004]

Who invented the names 'odd' and 'even' numbers? When did they first start being used?

History of Properties [12/11/2001]

Who invented the properties? For example, the distributive property and the associative property.

History of the Fraction Bar [09/01/2005]

What is the original name of the fraction bar? I know it is called the vinculum, but was that the original name? If not, what was it originally called?

History of the Mile [08/25/2002]

Why are there 5,280 feet in a mile?

History of the Order of Operations [11/22/2000]

Can you give me some facts and conjectures about when, where, and why the order of operations was established?

History of the Radical Sign [04/17/1997]

Who invented the radical sign?

History of the Root of an Equation [11/01/2007]

Why are solutions to equations referred to as roots?

History of the Word 'Exponent' [11/26/2003]

Who came up with the name 'exponent'?

History of the Word "Polynomial" [10/18/2006]

My teacher asked me to find the meaning of "mials" in the word polynomials. I know "poly" means "many" but what is the meaning of "mials" or "nomials"? And from which language did it come?

History of the y-intercept [03/18/2002]

Why does the variable 'b' represent the y-intercept?

History of Writing Decimals and Number Lines [10/28/1998]

Why, on a number line, are the negative numbers are on the left? When you deal with decimals, why are the whole numbers are on the left?

History of Zero and Place Value [02/17/1999]

Where were zero and place value invented or discovered?

How Can a Line Have Length? [04/14/1998]

If a Euclidean point has no length, how can a union of Euclidean points form a Euclidean line segment with length?

How Did Socrates Teach the Boy to Double the Area of a Square? [06/15/2010]

Reading Plato's Meno leaves a student confused about how the ancient Greeks scaled squares. Doctor Rick walks through this story of Socrates and his method, emphasizing that they would have approached this puzzle -- as well as the Pythagorean Theorem -- geometrically.

How Long is a Meter? a Second? [09/06/2001]

How is the length of a meter currently determined?

How to Use a Chinese Abacus [06/24/2004]

An introduction to how the abacus works and examples of entering, reading and adding numbers using it.

How Was the Pythagorean Thoerem Proved? [06/05/2006]

How did Pythagoras derive the Pythagorean Theorem?

Imaginary Numbers [10/11/1997]

Who invented the imaginary number?

Impossibility of Constructing a Regular Nine-Sided Polygon [04/07/1998]

Can you construct a regular 9 sided polygon with just a compass and straightedge?

Impossible Constructions [01/14/1998]

What are the three ancient impossible construction problems of Euclidean geometry?

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