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Dr. Math FAQ:
3D and higher
Browse Middle School History/Biography
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
About Roman numerals.
- Roman Numerals: Division [11/05/2001]
I have found information on how to add and multiply Roman numerals, but
have not found any information on how to divide or subtract.
- Rounding Pi [06/01/1999]
Can you prove that the value of Pi cannot be rounded down to 3.0? Is there an error in the Bible?
- Rule of Three [06/15/2002]
Please explain to me briefly (and with an example) the concept of the
rule of three.
- The Second Millennium [11/29/1999]
Does the second millennium begin with the year 2000 or the year 2001? How
does this relate to the math of counting numbers and subtraction?
- Short History of Geometry [09/15/2001]
Were there any people who helped to develop geometry besides Euclid?
- Simple Example of Ramanujan's Work [03/28/1999]
Ramanujan's contributions to the divisibility properties of partitions of
- Subtracting Roman Numerals [03/14/1999]
What are the rules for the "subtraction components" in writing Roman
- Theta [04/14/1997]
What is Theta? Does it have a constant value?
- Trachtenberg Mathematics [12/08/1996]
I've been looking for a book I had a long time ago on the Trachtenberg
System of mathematics.
- Trisecting a Right Angle [12/16/1996]
An explanation of how to trisect a 90 degree angle, plus some
- Trivia about Famous Mathematicians [05/21/1998]
Interesting facts you might not know about 18 famous mathematicians.
- Was 1 Ever Considered to Be a Prime Number? [02/29/2004]
I learned that a prime number was one divisible by only itself and 1,
but my 4th grader says that per her book a prime requires 2 different
factors. I note your Greek reference for 1 not being prime, which
would indicate that I'm wrong and there was no change in definition.
However, Ray's New Higher Arithmetic (1880) states, "A prime number is
one that can be exactly divided by no other whole number but itself
and 1, as 1, 2, 3, 5, 7, 11, etc." Can you tell me when this change
happened and why?
- The Welsh Vigesimal Number System [02/17/2003]
What can you tell me about the Welsh version of the Vigesimal Number
- What did the Romans contribute to math? [10/18/1996]
The Romans must have know a great deal of math to build their roads and
- What If There Was No Zero? [10/21/2003]
Why did it take so long to discover zero? Why did early civilizations
not need zero? How would math as we know it be different if there was
- What is a Sign? [04/21/2003]
Can you do anything in math without signs?
- What was Fermat's Last Theorem? [07/23/1997]
I wonder if you might take the time to explain Fermat's Last Theorem. I
am an undergraduate in mathematics, so an easy answer would be perfect.
- When Do We Need to Know Roman Numerals? [08/26/2003]
I have a student who does not see how learning Roman numerals will
benefit her. What advice can you give her to make this learning
experience more relevant to her life and needs?
- When in Rome, Know Your Place — Less a Written Notation for It [01/27/2015]
An adult wonders how Romans could have developed their rules for subtraction
absent place value. Citing their use of the abacus, Doctor Peterson distinguishes
between operating with the concept and representing it.
- Where did Fahrenheit and Celsius Come From? [07/26/1997]
How did scientists figure out the relation between two numbers that mean
the same thing, e.g. 0 deg C and 32 deg F?
- Where Does Pi Come From? [11/04/1996]
If pi is a ratio of lengths that can be measured only so accurately, how
can we know the value of pi so exactly?
- Who Invented Algebra? [06/07/2004]
Who invented Algebra?
- Who Invented Binary? [05/07/2000]
Who invented the binary system of numbers and when was it developed?
- Who Invented Integers? [11/29/2001]
And when were integers invented?
- Who Invented Pi? [5/6/1995]
Who was the first person to use pi?
- Who Invented the Square Root? [12/11/1996]
I've only seen long, stringy roots!
- Who was Hero (or Heron)? [11/12/1997]
I have been trying to find information on the Greek mathematician Hero.
- Why Base 60 for a Number System? [1/15/1995]
What were the Babylonians thinking of when they chose a base 60 number
- Why Does Order of Operations Work the Way It Does? [05/04/2004]
What is the logic behind order of operations? Why do exponents come
before the other operations, and why does multiplication and division
come before addition and subtraction? How was this all decided?
- Why Do We Need to Study Rational Numbers? [04/22/2008]
My students want to know why they need to know what rational numbers
are and what use they have in the real world.
- Why e? [11/02/1997]
Why the letter e for the number "e"? Why not another letter?
- Why Forty, not Fourty? [3/30/1996]
My 7th and eighth grade math classes from Rossville, Kansas have tried to
figure out why the number "forty" is spelled as it is and not "fourty"...
- Why Is a Circle 360 Degrees? [07/01/1998]
Why is a circle defined as 360 degrees?
- Why is the Word "Number" Abbreviated to "No."? [05/13/2002]
Why is the word number abbreviated to no.?
- Why Use X and Y for Variables? [10/23/2002]
Why do we use x and y for variables in an equation?
- Why Were Fractions Invented? [11/26/2007]
An overview of the history of fractions and the purpose they serve.
- The Woman Mathematician Hypatia [11/7/1995]
We're trying to find information on a mathematician named Hypatia.
- Writing Roman Numerals [11/10/2003]
What is the correct way to write the number 3000 in Roman numerals?
Can you write the answer as III with the bar over it, meaning (3 * 1000)?
- You Can't Trisect an Angle [7/16/1996]
Who proved you can't trisect an angle?