Ask Dr. Math

High School Archive

Browse High School About Math
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?

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Sugar Cubes and Coffee Cups [09/26/2002]

Given 20 sugar cubes and 3 cups of coffee, how many cubes must be put into each cup of coffee if there have to be a total of an odd number of cubes in each cup?

Talking About Zero, Absolute Zero and Negative Numbers [11/12/2003]

Are there any useful strategies other than temperature to introduce negative numbers, and also to teach about zero, its properties, and how they differ from those of absolute zero?

Times Greater Than, Times As Much As [05/02/1999]

A number is five times greater than x. Will this number be 6x or 5x?

Trig Based on the Unit Square [10/22/1998]

Why are the sine and cosine graphs defined in a unit circle? Why not a unit square or any other geometric shape?

Trig Function Domains [08/23/1999]

Which came first, trigonometry based on the simple triangle or trigonometry based on the triangle of the unit circle?

Trigonometry and Music [12/21/1998]

How is trigonometry used in music?

Trigonometry and Space Exploration [05/29/2002]

How does Trigonometry relate to space exploration?

Types of Numbers [10/30/1998]

How are the different types of numbers related? For example, what about counting, whole, rational, irrational, integers, prime, ... ?

Types of Variables [01/14/1999]

Can you explain the different types of variables, such as free variables and bound variables?

Undefined Geometry Terms [09/16/2001]

I know that they call point, line, and plane the undefined terms of geometry, but is there a way to give those terms a definition?

Use of Math in Various Careers [11/06/2004]

Just briefly, how is math related to history, poly sci, visual communications, business, and psychology? I am giving a persuasive speech to a group of college freshmen and I want to make them realize how important it is to have math in their background.

Uses of Logarithms [07/20/2002]

Who uses logarithms, and for what?

The Value of Two-Column Proofs [12/19/2000]

What is the point of learning two-column proofs?

What Can Math Do for Me? [11/24/2005]

I understand the math I'm doing in grade 11, but I can't imagine how I'm ever going to use it in real life. What's the point of taking math?

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 no zero?

What is an Algorithm? [10/21/2001]

Please define and explain algorithm, and include an example.

What is Math? [10/04/1997]

Is math a science, an art, or some other anomaly?

What is Math? [09/14/2001]

Mathematics as the study of abstractions.

What is Mathematical Modeling? [11/08/2002]

I am looking for documentation that would describe the difference between calculations and mathematical modeling.

What Is Mathematical Thinking? [03/08/2005]

A lengthy but interesting discussion on what constitutes 'mathematical thinking' as defined by NCTM Standards and in general.

What is Mathematics? [09/22/2000]

Please tell me the definition of maths.

What is Trigonometry? [8/20/1996]

What is trigonometry, and what is it used for?

What Motivates New Definitions? [02/06/2000]

Why do so many mathematical objects -- groups, fields, rings, vector spaces -- have nearly identical definitions and properties? Does every new object have to undergo some rigorous proof of its existence?

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 is the expression Q.E.D. used? [02/15/1999]

More on Q.E.D.

Who Invented Binary? [05/07/2000]

Who invented the binary system of numbers and when was it developed?

Why Do I Have to Learn This? [05/03/2004]

When, in the real world, would I have to find the roots of a quadratic equation?

Why Do I Need to Study Math? [04/05/2007]

I am a high school student who is college bound, but I am not going into a major involving math, so why should I have to learn math in high school? Why do I need to know it?

Why Do We Have to Study Math in School? [02/25/2005]

A freshman in high school questions the point of learning lots of math that he will never use in real life, and Dr. Ian replies with some interesting thoughts about the benefits of studying math.

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 is Math Interesting? [01/16/2001]

Why does math have to be so boring and hard?

Why Is Mental Math Important? [03/25/2004]

How can I convince a 14 year old girl who is in 8th grade the importance of mental math? I think that skills like mentally adding and subtracting 2 digit numbers and being able to estimate multiplying 2 digit large numbers are critical. My daughter's teacher says that such skills aren't needed because of calculators and computers.

Why is Pi Everywhere? [2/9/1996]

Why does pi show up in things that don't seem to be related to circles?

Why Learn Geometric Proofs? [02/27/2002]

Why are we taught geometric proofs if the vast majority of us will never use them?

Why Learn to Factor? [07/08/2002]

Why do I need to learn to factor expressions if I'm going to be a fashion designer?

Why Proofs? Definitions and Axioms [09/16/2001]

Why are proofs important in the development of a mathematical system like geometry?

'Why' Questions in Math [04/19/2002]

Is math a bad area for asking 'why' questions?

Why Should I Study Calculus? [03/04/2001]

I am starting an AP calculus class next year and I would like to know why I should study calculus.

Why Study Upper-Level Math? [10/10/2001]

I'm talking about pre-calculus, calculus, trigonometry, that sort of thing.

Why Use h and k for the Center of a Circle? [05/09/2000]

Why are k and h used in the equation (x-h)^2 + (y-k)^2 = 0 for a circle with center (h,k)? Why not j and f, etc.?

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