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Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Art and mathematics.
    Law and mathematics.
    Medicine and mathematics.
    Music and mathematics.
    Poetry and mathematics.
    What is mathematics?
    Was math invented or discovered?

About Basic Geometry [10/14/1998]
Who developed basic geometry? What is it used for? Who uses it?

Definition of Opposite Sides [01/18/2001]
What is the formal definition of 'opposite sides' of a polygon? Does a regular pentagon have opposite sides? Does a concave polygon have opposite sides? How can we define it consistent with our intuition?

Difference Between Math and Arithmetic [11/06/2001]
My students haven't heard the word arithmetic. No one seems to be able to tell the difference, if there is one, between arithmetic and mathematics. Is there a difference, and what is it?

Disappointed by Definitions: Where's the Deduction? [10/17/2015]
Finding definitions instead of proofs, an undergraduate enamored of logico-deductive reasoning reconsiders his choice of college major — and in the process, raises existential questions about mathematics. After several exchanges that delve into imagination, intellectual maturation, and whether math is discovered or invented, Doctor Peterson pulls the disenchanted student back from the brink.

How Can Math Be Made More Interesting? [08/30/2001]
What can I do to help me be more interested in math?

Mathematics and Intuition [07/10/2001]
Certain "puzzlers" in mathematical recreations defy our sense of experience, leaving you wondering if the answer to a problem can really be true. How to convince the intelligent non-believer?

Mathematics in the Applied Sciences [02/24/1997]
How do civil engineers and others use math in their work?

More Methodical Than Guessing [06/12/2017]
A young adult who prefers clear procedures struggles with guessing to calculate square roots and factor polynomials. Distinguishing between operations and algorithms, Doctor Peterson surveys a range of methods for finding roots and factoring — some of which require no guessing, others of which involve approximating — before emphasizing the intuition that develops with perseverance.

The Number e [6/3/1996]
Is "e" a number like Pi? How does "e" relate to continued fractions?

Purpose of Algebra [10/15/1996]
What is the purpose of algebra and who came up with the idea?

Rational and Irrational Numbers [11/12/1997]
Which set is bigger, the set of rational or irrational numbers?

Real-World Carpentry and Trigonometry [11/19/2002]
I'm trying to come up with a formula to calculate the height of an arc at the midpoint of the chord that defines it knowing only the length of the arc and the length of the chord.

Ten Commandments of Math [07/05/1997]
What are the Ten Commandments of Math?

The Third Millennium [01/23/2000]
When does the Third Millennium begin? Are there any inherent predictions or unverifiable assumptions within math?

Understanding Mathematics [07/25/1999]
I feel compelled to ask questions like "how can we prove that?" and then set out to prove it. Is there a name for the type of scrutiny I enjoy?

Unproven Fundamentals of Geometry [05/18/1999]
What are some important postulates or axioms that geometry cannot exist without, but cannot prove, either?

Was Mathematics Invented or Discovered? [01/01/2001]
I need to write a 1,000 word essay answering the question "was mathematics invented or discovered?" Can you provide me with some insights and references?

What is Calculus? [05/06/1997]
What is calculus and how does it work?

Who uses Calculus? [12/13/1995]
I was wondering how calculus is used: what professions, in what situations?

Why Does Math Need Proofs? [03/24/2000]
Why does math need to have proofs?

Why Is Math Important? [01/02/2002]
Some of it we don't need to know in the real world, so why do they teach us things we won't need to know?

Why Simplify Square Roots? [05/17/1999]
We have been trained to simplify square roots, but we are now looking at the reasons why we should continue to teach the process.

Why Study Practical Geometry? [04/26/1997]
What can I do to help my students to see just how important Geometry and all Math is?

Why There are 12 Tones in a Scale [12/28/2000]
Why are there 12 tones in an octave? Can you explain the significance or the equation r^n = 2^m? Also, what's so special about a fifth? Why should the scale be based on the fraction 3/2?

Wording Division Problems [08/10/1998]
How would you clarify the wording of division problems like "divide into" or "divide by"?

Year 2000 (Y2K) Problem [07/26/1998]
Can you explain the Year 2000 problem in layman's terms? Why is it so hard to fix?

Absolute Zero [10/24/2001]
Is there an absolute zero in math? In real life?

The Algebra that High School and College Share in Common [12/05/2016]
In modern algebra, a teen does not recognize any of the algebra that he learned in high school. Doctor Vogler emphasizes operations to explain the connection.

Ambiguity or Flexibility? [10/22/2003]
It seems that sometimes we use the not-equal sign to state an absolute inequality (two expressions always have a different value), and sometimes we just mean to say that two expressions are not always equal. Can you please clarify this apparent ambiguity? How do we know which meaning is being used?

Applications of Non-antidifferentiable Functions [01/29/1999]
What are some of the real life applications of the functions sin (x)/ x, e^(-x^2), and sin (x^2)?

Art and Mathematics [2/8/1996]
Do you know ways that art can be linked to mathematics?

Avoiding Careless Mistakes [01/30/2002]
How can I avoid careless mistakes?

Chaos [01/27/2001]
How can a butterfly flapping its wings in South America cause a tornado in Texas?

Characterization of Truth in Mathematics [11/07/2003]
A discussion driven by the question, 'What does it mean for a mathematical statement to be true - from the viewpoint of a working mathematician?'

Chefs and Algebra [02/05/2002]
I hope to become a chef someday, and I would like to know how algebra (specifically polynomials, the quadratic formula, factoring, etc.) could possibly relate to my future career and my life beyond high school.

Civil Engineering and Math [02/25/1997]
What forms of math or physics do civil engineers commonly use?

Computer Software for Writing Math Problems [05/12/2000]
How can you write mathematical problems on computers? Is there specialized software that incorporates all symbols, etc.?

Connecting Algebra and Geometry [07/11/2002]
What are the mathematical connections between algebra and geometry?

Context, Language, and False Equations [02/12/2001]
Is there such a thing as a false equation? How does the context in which it is set affect the truth of an equation?

Coping with Carelessness: Strategies, Stresses, and Mindsets [01/14/2016]
A high-performing student's penchant for carelessness becomes too serious to ignore. Doctor Floor weighs in with three observations.

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