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- Relatively Prime [10/07/1999]
What does the term relatively prime mean, and how can you determine if
two numbers are relative primes?
- Rhombus and Square Comparison [01/14/2004]
Comparison of the definitions of rhombus and square as a way to answer
the questions, 'Is a square a rhombus?' and 'Is a rhombus a square?'.
- Rhombus vs. Rhomboid [08/27/2002]
What is the difference between a rhombus and a rhomboid?
- Roughing It More Rigorously [12/02/2010]
A physics student wants to make sense of the various symbols used to represent "approximately equal to" -- as well as the phrase's mathematical meaning. Doctor Vogler produces two precise definitions while acknowledging that context, and personal preference, rule the day.
- Scientific Notation and Engineering Notation [10/22/2003]
What is the difference between Scientific Notation and Engineering
- The Second Octant [04/03/2002]
Where is the second octant? No one seems to know how to count the next
octants after the first.
- Set, Subset, Element [3/10/1997]
Please define: set, subset, member, element, intersection, union.
- Significant Non-Zero Digits [11/27/2001]
How many significant digits are there in a number with no non-zero
digits? Example: 00.000 Are there any?
- The Simplex Method [11/2/1996]
How does the simplex method work and what would I use it for?
- Simson Line [04/19/1999]
What is the Simson line?
- Sine, Co-sine, and Tangent: SOHCAHTOA [03/28/1999]
I am having trouble figuring out what to use when solving a triangle
- Snub Cube [08/08/1998]
What is a snub cube?
- Speed of Light [06/08/2001]
What's m s^-1? Why isn't it just m/s (meters per second) instead? What's
the little "-1" at the end?
- Sphere Surface Area Precision [04/22/2003]
How can the formula 4*pi*r^2 for the surface area of a sphere be
- Squaring the Circle [3/16/1996]
Where did the phrase "squaring the circle" come from? We found it in
literature and wonder about its origins and what it means.
- Stretching Definitions, and Compressing [08/04/2014]
Given counterintuitive definitions in his textbook, a teen seeks clarity around how to
describe the effect of the positive factor c in y = f(cx). Surveying other usages of "compress"
and "stretch" around the web, Doctor Peterson turns up inconsistencies.
- Sum of First n Natural Numbers [12/03/2005]
Factorial refers to the product of the first n natural numbers. Is
there a name and symbol for the SUM of the first n natural numbers?
- Surds [05/17/2000]
Where does the term "surd" for square roots come from?
- Surface Area and Volume: Cubes and Prisms [05/27/1998]
What is the definition of surface area and volume? What are the
differences and similarities between surface area and volume?
- The Symbol for Natural Log [06/28/2000]
Why is "ln" and not "nl" the abbreviation for natural log?
- Symmetry [04/29/2001]
What is symmetry?
- Terminology: Quadratic Equation vs. Quadratic Function [04/07/2004]
As I read various algebra books for high school kids, I find what
appears to be an inconsistent use of the words 'quadratic equation',
and I wanted to be sure I use it correctly myself. Is it correct to
call y = ax^2 + bx + c a 'quadratic equation', or a 'quadratic function'?
- Tesseracts and Hypercubes [05/22/1997]
Can you give me any good sources of information that a high school
geometry student would understand?
- Theta [04/14/1997]
What is Theta? Does it have a constant value?
- Ticking Off Congruence [02/06/2013]
A teacher's textbook, and his colleagues, all assume that if two geometric objects have
different tick marks, then the two angles or segments indicated must be incongruent.
Doctor Peterson unpacks the ambiguity, then warns against the larger error of reading
too much in sketches.
- Topology [05/10/1997]
What is topology? What is knot theory?
- Topology [03/19/2001]
What is topology?
- Traceable Mathematical Curves [10/27/1997]
Is there any way to tell just by looking if a curve is traceable or not?
Is there some property of a curve that will tell you this? Do curves have
- Transfinite Arithmetic [10/28/1997]
What is transfinite arithmetic? I pretty much know what it means, but I
am having trouble applying it to aleph-null.
- Transfinite Numbers [11/07/1997]
I know that Georg Cantor discovered transfinite numbers, but what are
- Translation [9/11/1996]
What does translation mean?
- Triangle Inequality Theorem [03/09/2001]
The lengths of the sides of a non-isosceles triangle, in size order, are
5, x, and 15. What are all possible integral values of x?
- Trilogy, Tetralogy... [05/28/2003]
Why isn't there a numbering system for groups like trilogies?
- Two Definitions of Limits, with Examples [05/11/1998]
Epsilon-delta definitions of the limit of a function and the limit of a
- Two Interpretations of Dimensionality in Geometric Figures [03/16/2004]
A line is 1 dimensional, a square or rectangle is 2 dimensional, and a
cube is 3 dimensional. My question is what if you throw in parabolas
or circles or the absolute value function, etc.? A circle is kind of
like a parabola, but it is very much like a square, so I am thinking
it is 2-dimensional. My conclusion is that the only 1 dimensional
object is a straight line, and a point is 0 dimensional, but I am not
confident that I am correct. Can you please clear this up for me?
- Undefined and Indeterminable ... at the Same Time? [09/05/2010]
A student wonders whether the labels "undefined" and "indeterminate form" could
apply to one and the same expression. Doctor Vogler considers several expressions,
functions, and limits to distinguish the different contexts that call for such terminology.
- Unit and Basis Vectors in Three Dimensions [05/09/1998]
Explanations and uses of unit vectors and basis vectors.
- Vertical Angles [10/27/1996]
What are vertical angles?
- Visualizing Skew Lines [05/16/2002]
What do you call lines that are not parallel but don't intersect?
- Volume vs. Capacity [05/01/2002]
Can you explain the difference between the terms volume and capacity?
Also mass and weight.