Math and Multimedia Carnival Criteria for Selection of Articles

The Mathematics and Multimedia Blog Carnival is now accepting articles  for the next issue. Although any math article might be accepted, below are the Revised Criteria for Blog Carnival Selection.  This will be characteristics of the articles that will be prioritized.  Articles with no links are done, but not yet posted.

1. Connection between and among different mathematical concepts

2. Connections between math and real life; use of real-life contexts to explain mathematical concepts

3. Clear and intuitive explanation of topics not discussed intextbooks, hard to understand, or  difficult to teach

4. Proofs of mathematical theorems in which the difficulty of the explanation is accessible to high school students

5. Intuitive explanation of higher math topics, in which the difficulty is accessible to high school students

6. Software introduction, review or tutorials

  1. Investigating Polyhedrons with Poly
  2. GeoGebra Tutorial Series

7. Integration of technology (Web 2.0, Teaching 2.0, Classroom 2.0), in teaching mathematics

  1. Using Google Sketchup in Teaching Mathematics
  2. Use of Google Docs  in Teaching Mathematics.

Mathematics and Multimedia Blog Carnival is still in its infancy, so please help spread the word about it. I would appreciate if bloggers who has benefitted from Mathematics and Multimedia, especially those whose article was accepted in the previous carnival, would announce it in their blogs.

To submit article the Math and Multimedia Blog Carnival, click  here.

The Math Teachers at Play Carnival and Carnival of Mathematics are also accepting math articles for their carnivals. Please do not duplicate submissions.

Erlina Ronda of Keeping Mathematics Simple will host the Mathematics and Multimedia blog carnival special edition on December 2010.  Her topic will be on Teaching Algebra Concepts. You can email her to submit in advance.

Photos: Wikipedia Concept Map by juhansonin, Mandelbrot Julia Section by Arenamontanus

Division by Zero

In studying mathematics, you have probably heard that division of zero is undefined. What does this mean?

Since we do not know exactly what is the answer when a number is divided by 0, it is probably reasonable for us to examine the quotient of a number that is divided by a number that is close to 0.

If we look at the number line, the numbers close to 0 are numbers numbers between –1 and 1.

Figure 1 – The number line showing the numbers close to 0.

For instance, several positive numbers close to 0 and less than 1 are 0.1, 0.01, 0.001 and so on. Similarly, negative numbers close to 0 but greater than – 1 are –0.1, -0.01, -0.001 and so on.

The table and the numbers below shows the quotient 1/x when 1 is divided by x, where the x’s are numbers close to 0.

Figure 2 – The value of 1/x as x approaches 0 from both sides.

In the graph, as x approaches 0 from the right (as x, where x are positive numbers, approach 0), the quotients of 1/x are getting larger and larger. On the other hand, as x approaches 0 from the left (as x, where x are negative numbers, approach 0), 1/x is getting smaller and smaller. Hence, there is no single number that 1/x approach as x approaches 0.  For this reason, we  say that 1/0 is undefined.

A simple analogy would also let us realize that allowing division by 0 will violate an important property of real numbers.  For example 8/4 = 2 because 2 x 4 = 8.  Assuming division of 0 is allowed. If 5/0 = n, then n x 0 = 5.  Now, that violates the property of a real number that any number multiplied by 0 is equal to 0.

Since division by 0 yields an answer which is not defined, the said operation is not allowed.

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