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- Euclidean Algorithms [3/13/1996]
What is the Euclidean algorithm? What is a "constructible" number? What
can you tell me about Diophantine equations?
- Euler Line [06/08/1998]
What is the Euler line?
- 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?
- Expressions vs. Equations, Explained [04/10/2011]
A student knows how to evaluate expressions and solve equations, but doesn't see the
difference between the two. Doctor Ian explains the distinction by way of an analogy to
phrases and sentences, illustrating throughout with examples, before leaving the
student with a mathematical statement for her to ponder further whether "an equation
is an expression with an equals sign."
- 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?
- Function Exponentiation Convention [04/21/2013]
A student seeks clarity on the meaning of f^2(x) and other expressions that juxtapose
functions and exponents. Doctor Vogler empathizes, outlining the differing
interpretations, before recommending contextual clues — and pointing up a
larger lesson about ambiguity.
- Functions: The Very Idea [04/08/2014]
A teen struggles to grasp what constitutes a function, and to reconcile the uniqueness
of two functions that differ in notationally or computationally trivial ways. Doctor
Peterson offers perspectives both abstract and concrete.
- 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?