Month: September 2010

Basic Concepts of Functions

High School Algebra, High School Mathematics

Note:  This is the second part of the Functions Series. To view the other parts, click the link below.

Part I: Introduction to Functions
Part II: Basic Concepts of Functions

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In the first part of this series, we have discussed that a function is a relationship between two sets where for each value in the first set, there is exactly one corresponding value in the second set. We have painted large cubes, cut them into unit cubes and found a pattern about the number of cubes with 3, 2, 1 and no painted faces.

Figure 1 – Cubes painted and sliced into unit cubes.

We found out that if a cube has side n units, if we painted all of its faces and cut it into unit cubes, the following relationships hold: » Read more

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Dominoes and Mathematical Induction

College Mathematics, Number Theory

Dominoes are Falling Down

If you queued ten thousand dominoes on a very long table and you want to let them all fall just by letting the first domino fall, then how would you queue it?

The best idea probably is to queue them such that:

  1. When the first domino falls, it will hit the second domino.
  2. Make sure that each domino will hit the domino next to it and that each hit domino will fall.
  3. If conditions (1) and (2) are satisfied, then all the dominoes will fall.

The domino effect

In fact, no matter how many dominoes we put on the table, as long as conditions (1) and (2) are satisfied we are sure that all the dominoes will fall. » Read more

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GeoGebra Essentials 2 – Constructing a Rectangle

GeoGebra, Software Tutorials

This is the second tutorial in the GeoGebra Essentials Series. If this is your first time to use GeoGebra, it is important that you read the Introduction to GeoGebra post. It is also important to read the GeoGebra Essentials 1. This tutorial is just a repeat of the GeoGebra Basic Construction 5, but I have put a more thorough discussion on free, semi-free and independent objects.

In the tutorial below, menu commands, located in the menu bar, are in green bold text, and the submenus are denoted by the > symbol. For example, Options>Labeling>New Points Only means you have to click the Options menu, choose Labeling from the list, then New Points Only. The tool texts are colored light red. For example, New Point means, the New Point tool.

In this tutorial, we  create a rectangle using the segment tools, the parallel line tool, and perpendicular line tool.  We learn how to measure the length of segments and angles. The output is of this tutorial is shown below. » Read more

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