Mathematics and Multimedia

A Simple Proof of the Arithmetic Mean Geometric Mean Inequality

Posted on May 16, 2012 by Guillermo Bautista | Leave a comment

Last February, we have used area to prove the Arithmetic Mean – Geometric Mean Inequality (AM-GM Inequality). In this post, we show a simpler proof.

Recall that the AM-GM Inequality states that given two numbers, their geometric mean is always less than or equal to their arithmetic mean. That is given two numbers $a$ and $b$ ,

$\displaystyle\sqrt{ab} \leq \frac{a+b}{2}$ . Continue reading →

→ Leave a comment

Posted in High School Mathematics, High School Number Theory

Tagged am gm inequality proof, arithmetic geometric mean inequality, mathematical proof

Microsoft Mathematics Tutorial 6 – The Unit Converter

Posted on May 13, 2012 by Guillermo Bautista | 1 Comment

This is the 6th tutorial in the Microsoft Mathematics Tutorial Series. In this post, we discuss how to use the Unit Converter of Microsoft Mathematics.

Microsoft Mathematics has a built-in unit converter that allows conversion of different types of measurements. It supports measurement conversion of length, area, volume, mass, temperature, velocity, pressure, weight, energy, power, time, and force.

To use the Unit Converter, do the following:

Click the Home tab and then select the Unit Converter button from the Tools group. This will display the Unit Converter dialog box as shown in the figure above.
In the dialog box , click the type of measurement you are converting in the Convert list (e.g. Mass).
Select the type of units that you are converting in the From and To list boxes.
Type the measurement that you are converting in the Input box.
Click the calculate button to convert.

You should notice while doing the tutorial that Microsoft Mathematics supports conversion between the metric and the English system in some categories; for example, in the weight/mass category, measurement in kilograms maybe converted to pounds and vice-versa.