## Probing Into the Past

If you are working with students on the number system, mention the origin of the place value system. Students will most likely find it surprising that the digits 0–9 first appeared in 1202, when Leonardo of Pisa, more commonly known today as Fibonacci, introduced them in his book,Liber Abaci(Sigler, 2002):The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these figures and with the sign 0, which the Arabs call zephyr, any number whatsoever is written.

A certain sentence in the Bible appears twice, identical in every respect except for the Hebrew word for “line measure,” which the two citations spell differently. Both 1 Kings 7:23 and 2 Chronicles 4:2 describe a pool in King Solomon's temple:And he made the molten sea of ten cubits from brim to brim, round in compass, and the height thereof was five cubits; and aline measureof thirty cubits did compass it round about.

## The Magic of Numbers

#### Figure 1. The Patterns in Mathematics

*why*they work. Show algebra students the following “trick.” Have each student select a three-digit number for which all three digits are different. Tell the students to reverse the digits of their three-digit number and subtract the smaller number from the larger. The students must then reverse the order of the digits in their answer and add this new number to the difference they got in the previous step. Ask one student to read out the answer. It should be 1,089. Other students will exclaim: “I got the same answer!” How can this be, when everyone presumably began with an individually selected number? The ensuing discussion can address the algebraic justification of this question.

## Zeros, Lines, and a Six-Inch Mouse

#### Figure 2. Dividing by Zero

#### Figure 3. The Tricks Lines Play on Us

Seemingly insurmountable problems can fascinate a class. The cleverness of the solution to the following problem—and its inherent elegance—will impress students.A rope is tied along the earth's equator, circumscribing the entire sphere. Now lengthen this enormously long rope by 1 meter. It is no longer tightly tied around the earth. If we lift this loose rope equally around the equator, uniformly spacing it above the equator, can a mouse fit beneath the rope?

## New Perspectives on Old Problems

When your students consider the following problem, how do they generally go about solving it?In a single elimination basketball tournament (where one loss eliminates the team), 25 teams are competing. How many games must they play until there is a single tournament champion?

*lose*in a tournament with 25 teams to produce one winner? The answer is, naturally, 24. So there you have it, simply done.