Problem of the Week: Sept. - Dec. 1995
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- September 4-15, 1995: What are the three most "geometric" objects in your house or neighborhood?
- September 18-22, 1995: What picture would prove what (a + b)^2 is equal to?
- September 25-29, 1995: Split a regular hexagon into three identical parts. What shape is each part? Split a regular hexagon into six identical parts, at least two different ways. What shapes are your pieces? Split a hexagon into six identical kites.
- October 2-6, 1995: Describe the "path" left behind by four different shapes (a rectangular parallelopiped, a sphere, a square pyramid, and a cone) when they're dipped in paint and rolled across a piece of paper.
- October 9-13, 1995: A bunch of unit cubes are put together to form a larger cube. Some of the faces of the larger cube are painted. Then the large cube is taken apart and 24 of the small cubes have no paint on them. How big was the large cube and which of its faces were painted?
- October 16-20, 1995: Thirteen matches are arranged to make six equal regions. Take away one of the matches and arrange the remaining twelve so that they still make six equal regions.
- October 23-27, 1995: A large cube is made up of 13 double cubes plus a single cube. What color is the single cube, and where does it have to be? How did you figure it out?
- Oct. 30 - Nov. 3, 1995: Emmitt Smith of the Dallas Cowboys football team took the handoff and ran toward the right sideline, eventually going out of bounds five yards downfield. What's the minimum distance he could have run?
- November 6-10, 1995: Using small blocks, start with an equilateral triangle. Put a square on each edge and connect the outside vertices of adjacent squares to form a hexagon. Is this hexagon equilateral? Is it
equiangular? What is its area if the edgelength of the original triangle is one unit? Extra: Will it tile the plane?
- November 13-17, 1995: In college softball, where the pitching rubber is 43 ft. from home plate, where should the rubber be in relation to the line between first and third? Should it be easy to tell if the rubber is in the wrong place? How about in high school, where the pitching rubber is 40 feet from home plate? How far is it from the tip of home plate to second base?
- Nov. 20-Dec. 1, 1995: Where should the anchor be so that my Thanksgiving turkey is an equal distance from the tree, the water, and the food? Will the six foot range be enough for him to reach everything he needs?
- December 4-8, 1995: In a tangram - a puzzle consisting of a square cut into seven pieces - which of the triangles are congruent to each other? If AB = 1, what is the area of each of the seven pieces?
- December 11-15, 1995: Two diagrams show "nets" of a cube. When you fold up the one on the left, what shape is made by the lines on the faces of the cube? How would you draw the lines on the net at the right so that they make the same shape?
- December 18-29, 1995: Assume a cube with an edgelength of 1. What is the perimeter of the largest rectangular cross section we could get out of such a cube? How did you get it? How could we get an equilateral triangle as a
cross section? What's the perimeter of the largest triangular cross section we could get?
On to 1996
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