# Monthly Archives: December 2012

## 2012 in review

The WordPress.com stats helper monkeys prepared a 2012 annual report for this blog. Here’s an excerpt: 600 people reached the top of Mt. Everest in 2012. This blog got about 9,300 views in 2012. If every person who reached the … Continue reading

## Diagonals in Octagons

How many more diagonals are in an octagon than in a hexagon? Source: NCCTM Mathematics Teacher SOLUTION We draw a diagonal by connecting two non-adjacent vertices. For example, is a diagonal but and are not. How many ways can we … Continue reading

## Difference of Squares

Evaluate . Source: NCTM Mathematics Teacher SOLUTION Let Without changing the value of we subtract and then add Answer:

## Most Beautiful Equation

The equation is often called the most beautiful equation in mathematics because it relates five of the most important numbers. Can you find an equation that relates , and . Source: NCTM Mathematics Teacher SOLUTION Answer:

## Sum of Three Squares

Find the four smallest distinct positive integers such that . Source: NCTM Mathematics Teacher SOLUTION Consider the square integers We form sets of square integers; find all possible three-element subsets of those sets; and see if the sum of the … Continue reading

## President Garfield

American president James A. Garfield devised an original proof of the Pythagorean theorem using the following figure. Can you complete the proof? Source: NCTM Mathematics Teacher SOLUTION Area of trapezoid = area of right triangle area of right triangle Area … Continue reading

## Square Pizza

If the price is the same, which is the better buy – a ten-inch round pizza or a nine-inch square pizza? Source: NCTM Mathematics Teacher SOLUTION Area of round pizza square inches Area of square pizza square inches square pizza … Continue reading

## Number of Subsets

The number of subsets in set is twenty-four more than the number of subsets in set . How many elements are in set ? Source: NCTM Mathematics Teacher SOLUTION Suppose and . Number of subsets in Number of subsets in … Continue reading

## Twelve Hour Period

In a twelve-hour period of time, for how many minutes is the number of the hour greater than the number of the minute? Source: NCTM Mathematics Teacher SOLUTION From to minutes From to minutes From to minutes etc. From to … Continue reading

## Volume of Rectangular Box

The areas of the sides of a rectangular box are , and . What is the volume of this box? Source: NCTM Mathematics Teacher SOLUTION Let represent the lengths of the sides. Eqs. and yield Simplify Cross multiply Substitute the … Continue reading