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- Definition of Negative Square Roots [03/08/2004]
I know that the square root of 49 = 7 since 7 x 7 = 49. But the
negative square root of 49 is -7. Is this because (-7) x (-7) also
equals 49 or because the square root of 49 is 7 and the negative stays
because it is not involved with the operation? My teacher wrote
-SQRT(49) = -7 because (-7) x (-7) = 49.
- 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?
- Definition of Oval [06/09/2002]
Can you give a precise definition of 'oval'?
- Definition of Set and How the Empty Set Fits within It [07/18/2004]
A set is defined as ďA collection of well-defined objects," and my
students have a hard time understanding how a collection can be empty
in the case of the null set.
- Definition of 'Solve' [11/29/2005]
In algebra class I was told that a problem such as 2 + 2 cannot be
solved. In order to 'solve' a problem there has to be a variable
involved. Is this correct?
- Definitions as a Tool of Mathematics [03/04/2003]
Defining polyhedra: regarding unusual polyhedra, how can we exclude
'doubled' shapes, e.g. two tetrahedra that join at a single vertex
(sort of like an hourglass)?
- Definitions of Advanced Concepts [11/13/1998]
Can you give me definitions for: Pythagorean Triplets, Principle of
Duality, Euclid's Elements, Cycloid, Fermat's Last Theorem?
- Definitions of Cones and Cylinders [03/02/2004]
Are cones and cylinders pyramids, prisms or neither? My 5th grade
geometry class cannot reach an agreement on this subject!
- Definitions of Edge and Face in 2D and 3D [10/10/2008]
What is the 'official' definition of 'edge'? Specifically, is an edge
restricted to the intersection of two non-coplanar faces or do two-
dimensional shapes have edges? I'm also curious about a definition of
'face'. How many faces does a two-dimensional shape have?
- Definitions of Monomials and Polynomials [03/11/2004]
Why is 1/x considered not to be a monomial? It could be written as
x^(-1) which is just one term. My math text says that it is NOT a
monomial but it does not say why.
- Definitions of Range [10/20/2003]
I can find only one definition of range in the math dictionaries -
the difference between the smallest and the largest number in a set.
We are always talking about 'They range in age from, or they range in
height, or they range in weight, or they range in size, etc'. If
the only defintion of range is the difference, why do we say 'They
- Degenerate/Nondegenerate Figure [10/27/2001]
We need to know what a nondegenerate circle is. (We're trying to decide
whether this is a model of incidence geometry, but don't know the
- Degenerate Triangle [09/03/2003]
Isn't a degenerate triangle really just a line segment?
- Degree of Constant Function [11/08/2001]
We think F(x) = 1x^0 is not a polynomial function (because polynomials
shouldn't have discontinuities), but F(x) = 1 is a polynomial. And F(x) =
1 still has degree 0 but for reasons we can't explain.
- Degrees and Radians, Explained [03/19/2002]
How do you find the degree measure for an angle from pi/60 rad?
- Degrees in a Sphere? Steradians [09/27/2001]
If one can say that a circle contains 360 degrees, how many degrees can
one say are in a sphere?
- Degrees of Freedom [12/17/2002]
What is meant by 'degrees of freedom'?
- The Degree Symbol [11/02/1998]
Do you know what the degree symbol stands for? What is its history?
- De Longchamp's Point [09/21/2000]
What is De Longchamp's point, and how is it used?
- Determinant of a Matrix [11/05/1997]
Can you give us a definition for the determinant of a matrix?
- Difference Between arsinh and arcsinh Functions [05/13/2004]
Why isn't there a "c" in arsinh, arcosh, and artanh? These are the equivalents of arcsin, arccos and arctan but they are hyperbolic.
- 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?
- Difference between Oval and Ellipse [10/18/2001]
What is the difference between an oval and an ellipse? Am I right if I
say that "all ellipses are ovals, but all ovals cannot be ellipses"?
- Differentiating Variables from Functions [02/03/2004]
How can you tell whether a letter stands for a variable or for a function?
- Dimensions [08/30/2001]
What are 1-dimensional, 2-dimensional, and 3-dimensional? What's the
- Disjunctive Syllogism [09/25/1998]
What is the Disjunctive Syllogism?
- Do Circles Have Corners? [08/06/1999]
Can you have angles or corners without edges?
- Do Cones and Cylinders Have Faces or Surfaces? [03/16/2004]
Are the sides of a cone or cylinder called faces or are they curved surfaces? I've seen different books with different answers. Some also say that a cone has no vertex.
- Does 2k4 Mean 2004 or 2400? [01/10/2004]
On internet communities it is common to reduce figures using 'k' as a
shortcut; for example 2k is used instead of 2000. I was under the
impression that a number after the k (such as 2k4) meant 2400, and
that to get 2004 in this system you'd need to write 2k004. But I've
also seen 2k4 used for 2004. Which is correct? Does 2k4 mean 2004 or
- Does a Cone have an Edge? A Vertex? [03/12/2002]
Our 4th grade math textbook defines a cone as "A solid figure with one
circular face and one vertex." This sounds reasonable until you read the
textbook's definitions for face, edge, and vertex.
- Domain and Natural Domain: What's the Difference? [01/13/2010]
Doctor Rick produces a function with an undefined value in its natural
domain -- then declares a more restrictive domain.
- Domain and Range of Functions [03/20/2003]
I am learning in school about the domain and range of functions. Why
are they called domain and range? And where did they come from?
- An Easy Definition of Calculus [9/4/1995]
What is calculus?
- Equilateral, Isosceles, Scalene - Word Origins [12/09/2001]
I need to find out about the origins of the scalene, isoceles, and
equilateral triangles. How they were named?
- Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]
What are the origins and roots of the words geometry, algebra, and
- Etymology of 'Asymptote' [05/13/2002]
Where does the term 'asymptote' come from?
- Etymology of 'Logarithm' [03/19/1999]
How does the term 'logarithm' relate to the terms 'exponent' and 'knots',
and to nautical logbooks?
- Etymology of the Word Asymptote [01/26/2001]
My math instructor has asked for the origin of the word asymptote....
- Etymology of the Word Hypotenuse [01/26/2003]
Why is the hypotenuse called 'hypotenuse'?
- Etymology of the Word Mathematics [12/10/2001]
Why do you call maths maths?