# Month in Review – July 2012

It’s the end of the month again. In case you missed some posts, here is the complete list of posts for July 2012. Enjoy reading!

Month in Review

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You might also visit my other blogs:

• Math Palette – a blog about math appreciation
• GeoGebra Applet Central –  a collection of GeoGebra applets.
• Sipnayan – My math tutorial blog written in Filipino.
• School of Freebies – A blog about free software and anything free on the net.

# Introduction to Number Bases

In Clock Arithmetic and Modular Systems, we have learned about a different number system, a number system whose largest digit is 12.  We observed that in that system, we can only use the numbers 1 through 12. We also noticed that 12 acts as 0 since 12 added to any number is equal to that number.  If we  change 12 to 0, we can only use 0 through 11 as digits.

The number system that we use everyday, the decimal number system, uses 0 through 9 as digits. In the decimal number system, if we add 1 to the largest digit which is 9, we add 1 to the number on next place value and write 0. For example, 9 + 1 = 10 and 10 means that 1 tens and 0 ones. In the decimal number system, 325 means 3 tens squared (or hundreds), 2 tens and 5 ones. Using the expansion notation, we have Continue reading

# Why Expressions with Negative Exponents Equal their Reciprocals

We are familiar with the rule that for a positive exponent $m$,

$x^{- m} = \displaystyle\frac{1}{x^m}$

and

$\displaystyle\frac{1}{x^{-m}} = x^m$.

In this post, we learn the reason behind the concept of negative exponents and their relationship to the reciprocal of the algebraic expression containing them.

Recall that in dividing an algebraic expression with the same base, we have to subtract their exponents. For example, for $m > n$ Continue reading

# Wholemovement and The Art of Folding Circles

Last week, I discovered Wholemovement, an interesting origami site about folding circles. The site highlights the beauty of circles and exhibits variety of 3D shapes that can be constructed from it.

To those who want to try the basics, you can read how to fold circles. The page includes procedures on creating a sphere, a tetrahedron, an octahedron, and an icosahedron using a circle. You may also want to explore the Gallery page to view more complicated folds.

Paper folding is closely related to mathematics. We can consider creases as lines, and intersections as points. Folding papers emphasizes congruence, symmetry, and transformation.

To those who are interested in this topic, check out Professor Kazuo Haga’s book Origamics. It is an excellent resource on the mathematics of problem solving.

# Who’s the Winner?

Five students have just completed a logic contest. Lois Lang,  a school reporter and last year’s logic contest champion, asked for an interview.

Oh, this is giving me a headache!

Th students decided to test Lois Lang. Each student agreed to make one true and one false statement during the interview.

Frances: Kai was second. I was fourth.
Leyton: I was third. Charles was last.
Denise: Kai won. I was second.
Kai: Leyton had the best score. I came in last.
Charles: I came in second. Kai was third.

Help Lois Lang determine the winner.

Adapted from Discovering Geometry