The Three Meanings of Similarity

We can say that two objects are similar if they look alike. In layman’s words, objects with the same shape, whether they have the same size or not are usually called similar. In mathematics, it is quite different. In this post, we are going to learn the three mathematical meanings of similarity.

In mathematics, two objects are similar when either one of the following three conditions is true.

1. When one figure is reduced or enlarged, it will become congruent with the other

The first meaning is based on the definition of congruence. That is, when two figures are similar, if one figure is enlarged or reduced, then they will become congruent with the other. This definition is better illustrated graphically, using a drawing or an applet just as the one shown below.  Continue reading…

 

GeoGebra for iPhones is now online

For iPhone users, the long wait is over. In case you missed it (I missed it actually), GeoGebra has released the GeoGebra Graphing Calculator for iPhones last December. I have only personally used the app for a week and I’m really satisfied with its performance and speed on my old iPhone 5.

image via GeoGebra blog

For those who have not tried GeoGebra, it is a free and open-source software for teaching mathematics. We have a lot of tutorials about it here which I’m going to update to the current version of GeoGebra this year.

GeoGebra is available for desktop computers, tablets, and Android phones. It comes on multiple platforms including Windows, Mac, and Linux. You can also install it in the Google Chrome app.

 

Introduction to the DaMath Board Game Part 3

This is the third part of our series on learning how to play Damath. In the first part, we learned about the basics of Damath and in the second part, we learned how to capture multiple pieces.

The Dama Piece

A piece can be promoted when it reaches the last row (the first row of the opponent’s area) on the board. In the next figure, if it is the Red Player’s turn, then he can promote 2 by moving it to (6,7) as indicated by the arrow. In the same way, the Blue Player’s 8 is just two moves away from being promoted. Promoted pieces are called dama (roughly equivalent of Queen in chess). Each player can have more than one dama.

Moving the Dama

The dama can move forward and backward on unobstructed diagonals. For example, if the Red Player’s 2 becomes a dama on (6,7) as shown in the next figure, it can move to any of the four squares indicated by the red lines. It cannot move to (1,2) and (0,1) because 8 is obstructing the path.  Continue reading…

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