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Geometry Forum Project of the Month         Triangle Pentomino

Project of the Month: Oct. 1996 - May 1997

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  1. October 1996 - Pentominoes
    A pentomino consists of five unit squares stuck together so that each square shares at least one whole side with another square. There are 12 types of pentominoes. Your tasks: 1. Find the other 11 types of pentominoes. 2. Find all different rectangles with integer sides greater than 2 whose area equals 60. Show that each of these rectangles can be exactly covered (tiled) by the set of 12 pentominoes. You are allowed to rotate and reflect the pieces to tile the rectangles.

  2. November 1996 - How many cubes will be painted?
    A cube with sides n units long is painted on all faces. It is then cut into cubes with sides 1 unit long. Explain how many of these smaller cubes will have paint on: a) 3 surfaces b) 2 surfaces c) 1 surface d) no surfaces

  3. December 1996 - How does a rangefinder work?
    Rangefinders are like binoculars. They are about 10" long with two windows on either end that face the animal. You look through the viewfinder on the back with one eye. You see two pictures of the animal. You turn something until the two images are on top of each other. The rangefinder tells you how far away the animal is. How does it work? How can it figure out how far away the animal is?

  4. January 1997 - Overlapping polygons.
    When two congruent 10cm x 10cm squares overlap with the vertex of one square at the center of the other square, the overlap will always be 25 cm^2. Is the same true for other polygons like triangles, rectangles, or pentagons? Would the figures have to be regular polygons? What about a rhombus?

  5. February 1997 - Midpoints of Quadrilaterals
    What figure is formed when the consecutive midpoints of the sides of a quadrilateral are joined? What if the original quadrilateral were a rectangle? A kite? An isosceles trapezoid? A square? A rhombus? Other shapes?

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