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- Examples and Explanations of Basic Properties of Equality [07/31/2004]
Can you explain the substitution, symmetric, and transitive properties
of equality in simpler terms?
- Explaining Independent and Dependent Variables [10/25/2002]
Can you elaborate on the definitions of independent and dependent
- Explaining the Determinant [11/16/1997]
I am trying to understand what the determinant of a matrix actually is.
- Explain Supremum [02/02/1998]
Can you please explain, perhaps with an example, the concept of
- Explanation of Orientation in Transformations [05/24/2007]
We've been learning about transformations and my teacher says that a
translation, rotation, and dilation all preserve the orientation. I'm
confused as to what orientation is. Could you explain it?
- Expression vs. Equation [03/20/2003]
What is the difference between an expression and an equation?
- Factorial Notation [9/8/1996]
What is 7!?
- Fibonacci sequence [1/28/1996]
What is the explicit formula for the Fibonacci numbers?
- Finding a Locus of Points from a Description [03/30/2004]
I am trying to help my son figure out these three questions, but we
aren't sure what is meant by "locus". Is there a formula to use?
- Finding the Next Number in a Sequence Given Its Geometric Mean ... Which Is a Square Root [09/24/2009]
A student who knows how to calculate geometric means gets rattled when
trying to determine a sequence from its square root geometric mean.
- Flavors of Facts [10/03/2003]
Is 1+1=2 a fact, or is it open to interpretation?
- The Fourth Dimension [8/24/1995]
What is the fourth dimension mathematically?
- Fuzzy Logic [04/26/1997]
What is fuzzy logic?
- General Comments on Standard Deviation [01/15/2004]
Answers to general questions about standard deviation including
vocabulary, interpretation, calculation, and history.
- Golden Triangle: An Isosceles Triangle [01/23/2001]
What is the Golden Triangle?
- Golden Triangle: What is It? [09/19/1999]
What is a Golden Triangle?
- Grad as a Measure of an Angle [03/20/2002]
I would like to know about the origins, use in the past, and whether (and
how) the grad is used now.
- Grouping Symbols [08/27/1998]
I need the names of four grouping symbols. I already know of parentheses
and brackets so that takes care of two...
- Harmonic Mean [12/15/1996]
What is the harmonic mean and how do you use it?
- Hexagon vs. Hexagram [01/11/1999]
What is the difference between a hexagon and a hexagram?
- History and Applications of the Natural Logarithm [03/02/1998]
I'm so surprised at how often the number e comes up. Where did it come
from? Who first derived it? Why is it so common in the field of biology?
- History of Abscissa [03/26/2001]
Where does the word abscissa come from?
- History of the Symbol for "Therefore" [11/14/2005]
Why is it that the symbol for "therefore" is a centered dot with two
lower dots? Where did that symbol come from?
- History of the Word 'Exponent' [11/26/2003]
Who came up with the name 'exponent'?
- History of the Word "Polynomial" [10/18/2006]
My teacher asked me to find the meaning of "mials" in the word
polynomials. I know "poly" means "many" but what is the meaning of
"mials" or "nomials"? And from which language did it come?
- How Are Functions and Expressions Related? [07/09/2004]
What is the relationship between a function and an expression? I
don't see any relationship, they are two completely different things.
- How Can a Set Be Empty? [09/29/2003]
Why is the empty or null set called a set when it has no elements?
- How Many Edges in a Circle? [06/15/1999]
Are there one, none, or an infinite number of edges in a circle?
- How the Trig Functions Got their Names [12/14/1997]
I can guess why three of the trig functions are called cosine, cotangent,
and cosecant. But why were the other three named the sine, the tangent,
and the secant?
- The Idea behind z-scores, and Their Relation to Standard Deviation [06/24/2010]
A student familiar with the definition of z-scores wonders why we use standard
deviations to calculate them. Illustrating two ways, Doctor Peterson explains the
concept of scaling that motivates this statistical measure.
- Identity and Inverse Properties for Zero [01/07/2004]
If we subtract 0 from a number and get the same number, doesn't that
make 0 an identity for subtraction? Also, can't a number be its own
inverse for subtraction?
- Implicit Functions [11/26/1997]
Please give me a definition and several examples of an implicit function.
- Incenter, Orthocenter, Circumcenter, Centroid [01/05/1997]
I have been having trouble finding the Euler line of a triangle.
- Inclusive and Exclusive Definitions [04/05/2001]
Are squares rectangles? Are rectangles squares?
- Inclusive Definitions: Trapezoids [11/04/2004]
As far as I know, a trapezoid is defined as a quadrilateral with exactly one set of parallel sides. However, a very highly regarded educator and textbook author recently argued that this definition is incorrect. His definition of a trapezoid is that it is a quadrilateral that has at least one pair of parallel sides. A square, therefore, would be considered a trapezoid. Is he correct or are thousands of books going to be published with the wrong definition?
- Inclusive vs. Exclusive Definitions [01/24/2002]
My geometry teacher says that a square is not also a rhombus, a
rectangle, and a parallelogram. Please help!
- Incommensurable Numbers [07/25/2001]
What is an incommensurable number?
- (In)consistent and (In)dependent Systems [01/02/2007]
Systems of equations are classified using the terms consistent,
inconsistent, dependent, and independent. I'm curious how those terms
were chosen and how they fit the solutions of the systems.
- Interpolation and Extrapolation [08/10/1999]
Can you give me a step-by-step procedure for finding missing values based
on interpolation and extrapolation?
- Interpreting Expressions Involving Cosine Squared [03/16/2007]
I don't understand the difference between cos(x)^2, cos^2(x) and (cos
(x))^2. Are they all same?