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- Complete This Square: x^2 + y^2 - 6x + 2 = 0 [03/16/2003]
I thought completing the square only involved quadratic functions,
such as f(x) = ax^2 + bx + c = 0. This question relates to the
equation of a circle...
- Computers: Defining Logical Operations [05/21/1998]
Can you tell me the meaning of the following logical operations: AND, OR,
XOR, NAND, NOR, NOT?
- Concept of Factoring [03/22/1997]
Could you explain the concept of factoring and give examples of its
- Congruence Symbol [05/23/2003]
How does congruence (3-lined symbol) relate to equality (=)?
- Conical Vertex? [03/27/2003]
What is the point at the tip of a cone called?
- Conic Sections and Parallel Lines [3/18/1995]
Our teacher told us there was a way to cut a cone with a plane to get
parallel lines. Another teacher in the department can do it
algebraically, but no one can do it physically. Is there such a plane in
reality or only in theory?
- Conjectures vs. Hypotheses [01/12/1999]
What is the difference between the terms 'conjecture' and 'hypothesis'?
Should the Riemann hypothesis be the Riemann conjecture?
- Contrapositives and Monotonic Functions [03/17/2003]
Defining 'monotonic' (increasing or decreasing functions) and
- Coordinate Systems [04/22/1997]
What is the polar coordinate system and how does it differ from the
rectangular coordinate system?
- Coordinate Systems, Longitude, Latitude [04/19/1997]
Can you explain pitch, roll, and yaw to me? Are there other systems for
measuring an object's position in space?
- Correct Usage of Equal and Equivalent in Math Statements [02/20/2008]
Is there a mathematical difference between "equal" and "equivalent"?
- Counting Collinear Sides [04/12/2013]
A student wonders how to count the sides of a polygon that has degenerate vertices.
Citing Wikipedia and MathWorld, Doctor Peterson teases out the various conventions.
- Covariance [02/05/1997]
What does covariance represent?
- Cross-Section of a Prism [08/02/2001]
Please define cross section, and explain the formula for the volume of a
- Cute Numbers [08/29/2003]
I have found two definitions of a cute number. Which is correct?
- Defining a Square Centimeter [04/09/2002]
Why is the area of a unit square the product of the two sides?
- Defining Decimal Numbers [07/01/2004]
An interesting look at how the idea of a 'decimal' number is widely
misunderstood and the word itself is used incorrectly.
- Defining Exterior Angles of Polygons [06/24/2004]
My math teacher says the sum of the exterior angles of a triangle is
900 degrees (360*3 - 180). I think that the sum is 360 degrees. Who
- Defining Modulus [12/10/2002]
I understand when this term is used to describe the congruent b-c
relation as mod (b,m), but why when we apply it to graphs does it
translate as 'absoluted/directed value of'?
- Defining Multiplication [08/16/2002]
What is the distinction between 3*4 and 4*3?
- Defining Positive Zero [03/07/2003]
The definite integral of f(x) from 0 to x has exactly one positive
zero at x = a. What's a 'positive zero'?
- Defining Probability [4/30/1996]
Is a probability number equal to a percent or a decimal?
- Defining Relative Error [03/11/2004]
I've seen "relative error" defined both as "the absolute error divided by the true measurement" and "the greatest possible error divided by the measurement itself." These definitions seem to be inconsistent. Which one is correct?
- Defining the Arcsinh Function [08/09/2003]
Find an exact value for x in: 4 sinh x = 3
- Defining the Complement of an Angle [08/04/2007]
If the complement of x is 90 - x, the complement is negative for x
greater than 90. I've seen conflicting definitions of the complement,
some saying it cannot be negative and others placing no restrictions.
Which is correct?
- Defining 'Undefined' [09/15/2003]
If a function is 'undefined at x', does this refer only to vertical
asymptotes, or to other discontinuities as well?
- Definition and Origin of the Word "Radical" [06/22/2005]
I'm curious what the exact definition of "radical" is and also where
and when the word originated.
- Definition For Cylinder without Big Words [11/03/1998]
I just need a good definition for cylinder that I can understand.
- Definition of a Cone [07/13/2000]
I don't see how a right circular cone cut parallel to the axis of
symmetry reveals a hyperbola. Shouldn't it be a parabola?
- Definition of an Ellipse [1/4/1995]
I have a question concerning the concept of an ellipse. It is said that
the equation for an ellipse is Pf + Pr= 2a where P is a point on the
ellipse and f and r are the points of the foci. How do we know that this
is true, that is that Pf + Pr = 2a? How did we come up with the constant
- Definition of an Identity Matrix [08/09/1999]
Which of the following would be an identity matrix?
- Definition of a Rolling or Moving Average [03/05/2004]
When someone says they have calculated a "rolling average," what
exactly does that mean? I cannot find the definition in any math books.
- Definition of a Tangent [10/27/1995]
What is the tangent of an angle?
- Definition of Equal and Equivalent Sets [05/31/2004]
Write a set that is equivalent to, but not equal to, the set (a, b, c,
d, e, f). Would the answer be all the same letters, just arranged in
a different order?
- Definition of Floating Point Data [07/02/2001]
What are 'floating point data'? How do they differ from an integer? What
are some examples?
- Definition of Fractal [01/17/2005]
What is the definition of a fractal? Would a circle be considered a
- Definition of Monomial [04/26/2004]
Do monomials include quotients of variables? For example, would x/y
or xy^-2 be considered a monomial?
- 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'?