# Monthly Archives: July 2014

## 2008 in Base 2

Express the integer in base . Source: NCTM Mathematics Teacher 2008 SOLUTION Please refer to the problem “Sum of Powers of Two” for details. In base Answer:

## Midpoints of Triangle Sides

Points , and are the midpoints of the sides of triangle . Find the coordinates of the points , and . (Labels , and are arbitrarily assigned to coordinates). Source: NCTM Mathematics Teacher 2008 SOLUTION Draw a first line passing … Continue reading

## 2008 As Sum of Consecutive Integers

The number can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of . Find the smallest of these consecutive integers. Source: NCTM Mathematics Teacher 2008 … Continue reading

## Rain Gauge

To create a rain gauge, a funnel having a diameter of inches is placed on top of a tall cylinder having a diameter of inches. How far apart should the -inch marks on the cylinder be placed? Source: NCTM Mathematics … Continue reading

## Koch Snowflake

A Koch snowflake begins with an equilateral triangle with a side length of (stage 0). Trisect each side and attach a smaller equilateral triangle to the center of each side (stage 1). Repeat for each triangle to obtain stage 2. … Continue reading

## Parabola Passing Through Three Points

Three points , and form the vertices of an equilateral triangle. Find the equation of the parabola that passes through these three points. Source: NCTM Mathematics Teacher SOLUTION is the vertex and the focus of the parabola. Let be the … Continue reading

## Midpoints of Four Sides

The midpoints of four sides of a regular hexagon can be connected to create a trapezoid, a kite, or a rectangle. Which two quadrilaterals formed in this manner have equal areas, and what fraction of the hexagon’s area do they … Continue reading