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- 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.
- Ways to Remember the Meaning of Circumference, Radius, Diameter, and Chord [03/18/2004]
If the minute hand touched the edge of the clock, would it be most
like a diameter, radius, circumference, or chord of a circle? I have
a hard time remembering what each of those means.
- What Are Differential Equations? [12/17/2003]
Can you please tell me what differential equations are? Why do they
have two variables? Why are the solutions formulas and not numbers?
- What are Flops? [02/25/2001]
What are flops, as relating to computers?
- What Are Proofs? [08/12/1997]
I am homeschooling and do not understand proofs. Can you help me out?
- What Are Quadratic Functions? [02/27/2003]
What is the difference between a quadratic function and a quadratic
- What Are the Definitions of Zero and Root? [12/23/2003]
What is a zero, and what is a root? How are they used with regard to
equations? Different sources seem to be giving me different answers,
some of which contradict each other. What actually IS a root or zero?
- What Constitutes a Prism? [06/10/1999]
If I am looking at an object that's shaped like a triangle, how do I know
if it's a prism?
- What Does a Twofold Increase Mean? [01/23/2004]
Is a twofold increase simply twice the amount? What about a threefold
increase? I'm not used to this terminology of using 'fold.' Does it
refer to powers or multiples?
- What Does Average Mean? [12/05/2001]
Can someone explain what average is? For example what is the average
rainfall in New York? I understand the formula needed to find the
average, but what is the meaning of average?
- What Does a Vertical Bar Mean? [01/29/2001]
I want to know what the symbol | means, for example |2+3|.
- What Does EE Stand For? [01/14/2003]
What does the EE stand for on a scientific calculator?
- What Does "Stellated" Mean? [03/31/1998]
Stellating polyhedra, including solids that are already stellated.
- What is a continued fraction? [03/06/1998]
What is a continued fraction and what makes it different from the types
of fractions or ratios I'm used to?
- What is a Cuboctahedron? [01/02/2001]
What is a cuboctahedron?
- What is a Functional Transformation? [08/11/2002]
I would like a brief definition of a functional transformation and
what an application is in early Calculus.
- What is a Median? [03/03/1998]
A definition of median, and four examples of calculating medians.
- What is an N-gon? [06/01/1998]
Can you explain the statement: "In an N-gon, n-3 diagonals can be drawn
from one vertex"?
- What is a point? [8/26/1996]
Define a point, please.
- What is a Property? [11/29/2001]
I understand Undefined and Defined terms and Axioms and Theorems, but
what exactly is a Property? Is it the same thing as a Theorem? Also what
is a Law?
- What is a Set? [04/04/1997]
What is the correct term to refer to groups of objects like 3 cars, 7
pencils, or 5 apples?
- What is a Sign? [04/21/2003]
Can you do anything in math without signs?
- What is a slide rule? [07/27/1997]
What does a slide rule do and how does it work?
- What Is a Theorem and Why Are They Important? [08/15/1997]
I don't understand how theorems help us learn.
- What is Dimensional Analysis? [11/26/2001]
What is dimensional analysis and how does it work?
- What is Length in a Rectangle? [05/31/1999]
Is the length of a rectangle the longest side, whether vertical or
- What is Math? [10/04/1997]
Is math a science, an art, or some other anomaly?
- What is Meant by "the Sum of a Series"? [10/21/2003]
A series is the sum of consecutive terms. So why do many authors
speak about "the sum of a series" if the name "series" already means
"sum of consecutive terms"?
- What is the Definition of 'Number'? [01/26/2006]
I think of a number as a symbol for a measure of magnitude, like how
many of something there are. You can't have 2 + i things, so how can
that be a complex 'number'? How do you define what a number really is?
- What Motivates New Definitions? [02/06/2000]
Why do so many mathematical objects -- groups, fields, rings, vector
spaces -- have nearly identical definitions and properties? Does every
new object have to undergo some rigorous proof of its existence?
- What Skew Lines Are and Aren't [01/14/2004]
A description of skew lines including diagrams and definitions.
- When is the expression Q.E.D. used? [02/15/1999]
More on Q.E.D.
- Why Cubed? [11/27/2001]
Why do we use "cubed" for the volume of a figure?
- Why Does 0^0 = 1 and Not Undefined? [11/30/2007]
Your proof for why x^0 = 1 uses a law which breaks down at x = 0. Then
in your definition for 0^0 you side significantly in favor of 0^0 = 1
based on your rule for x^0 = 1 (which was based on a law that breaks
down at 0). Based on what I've read I would side in favor of
undefined. Are there any more conclusive reasons for siding with 0^0 = 1?