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- 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?
- Introduction to Quadrants in the Coordinate Plane [02/05/2004]
What is a quadrant? How do you find it? I had to identify 9 ordered
pairs on a graph. Now I need to also name the quadrant each one is in.
- Inverse of a Function vs. Inverse Proportionality [11/20/2002]
Finding the inverse of a function and graphing yields a graph that has
been reflected in the line y = x relative to the function. Inverse
proportionality, however, yields a reciprocal relation graphically.
Why do these two things have similar names yet mean different things?
- Inverses of Functions, and Inverse Functions [02/12/2014]
A student's textbooks give her conflicting definitions about functions and their
inverses. Doctor Peterson makes sense of the disagreements by providing the bigger
- Is a Circle a Polygon? [03/07/1999]
A circle is not a polygon.
- Is an Equilateral Triangle Also Isosceles? [02/19/2008]
Can equilateral triangles also be classified as isosceles? In other
words, does an isosceles triangle have exactly two equal sides or at
least two equal sides?
- Is a Sphere 2-D or 3-D? [8/8/1996]
Is a sphere a two- or a three-dimensional object?
- Is Kite the True Name? [03/29/2002]
Is kite the true math name for this shape, or is there another?
- Isomorphisms [08/16/1999]
Can you give me an explanation and a nice example of isomorphism?
- Is Zero Considered a Pure Imaginary Number (as 0i)? [12/02/2003]
In the complex plane, zero (0 + 0i) is on both the real and pure
imaginary axes. Is 0 therefore a pure imaginary number as well as a
- Is Zero Really a Number or Just a Concept? [09/15/2005]
I've been taught that infinity is just a concept, not an actual
number. I'm wondering if the same thing can be said of zero?
- Josephus Problem [04/18/2003]
Every other person at a table is eliminated until there is only one
person left. Who is the survivor?
- The Königsberg Bridge [5/20/1996]
Do you have information on Konigsberg's bridge?
- Lagrange Multipliers [01/08/1998]
I have a problem with Lagrange Multipliers - can you help?
- Larger Than and As Large As [08/01/1999]
If the percussion section has 6 people, does the expression "the brass
section is three times larger than the percussion section" mean that the
brass section is 3*6 = 18 people or 4*6 = 24 people?
- Latin Origins of Trig Functions [11/20/1998]
What are the etymologies of the six trigonometric functions: sine,
cosine, tangent, cosecant, secant, and cotangent?
- Laws of Arithmetic [02/12/1999]
The Distributive Law, Associative Law, Identity, and Commutative
- Leg of a Triangle [04/02/2002]
I need to know where the name "leg" of a triangle comes from, or what its
- Length of a Light-Year [1/31/1996]
How far is a light year in miles or kilometers?
- Limit of x sin(1/x) [04/23/2002]
I assumed from the graph that the function had a limit at x=0 of 0,
but since it involves sin(1/0) I can not prove this using the basic
trigonometric limits (sin x/x and (1-cos x)/x), L'Hopital's
rule, or by rearranging the equation. Can you help?
- Linear Algebra - Definition of Orthonormal [10/28/1997]
Show that the transition matrix P from one orthonormal basis to another
is unitary, that is, P*P = I.
- Linear and Board Feet [01/04/1999]
Can you explain the terms linear foot and board foot as they are used in
the lumber industry?
- Linear Footage [04/20/2002]
There is a fence I want to buy, but the ad says '4 foot tall, 50
linear feet. What is a linear foot compared to a regular foot?
- Line of Best Fit [8/1/1996]
Are a best-fit line, a line of best fit, and a fitted line synonymous?
- Line of Best Fit, and Flight [02/04/2015]
What do "extrapolation" and "interpolation" mean? What are their purpose? Doctor
Peterson defines the terms, then gives real-world examples based on tracking the
flight of his son's recent airplane trip.
- Line or Ray Longer? [12/11/2001]
Which is longer, a ray or a line?
- Locus [05/03/1999]
What is a locus?
- Mass and Weight [08/16/1997]
Why are mass and weight both measured with the same unit? If weight is
different on the moon and mass is not, what is the difference?
- Mass versus Weight [09/09/99]
Do mass and weight refer to the same thing on earth? Is mass equal to
- Mass vs. Weight [01/22/1999]
Can you give me a definition of mass and how it differs from weight?
- Mathematical Induction [09/07/1998]
What is mathematical induction? Can you give an example of the ideas of
- Mathematical Meaning of Undefined [12/19/2002]
What is the meaning of the word 'undefined' in mathematical terms?
- Mathematical Models [07/17/2002]
What is a mathematical model, and how would it be used?
- Mathematics, Logic, and Intuition [05/27/2003]
How is math related to logic and intuition?
- Math Symbol for C [12/15/1997]
I am puzzled by one symbol of typing math. What does the upper case
letter C mean? As in (2C1) (3C1) / (47C2) = 6/1081.