January 2-5 - Bracing a Gate: I have two gates in my yard. One has a diagonal brace. What purpose does this brace serve? Why can't the gate just be a rectangle?
January 8-12 - Snow Pyramids: The man who plows the airport runway makes beautiful square pyramids of snow. Each edge of the base of one of these pyramids is 50 yards long. How tall are they? If he plows an area 50 yards wide and a mile long and the snow is 30" deep and he makes four pyramids, how tall is each pyramid?
January 15-19 - Scale Drawing: In making a drawing to scale of our 11'3" by 16'2" kitchen, what scale should I use if I want the drawing to be as big as possible and still fit on one 8.5" x 11" piece of paper? How wide will a standard (24" deep) kitchen counter appear in the drawing?
January 22-26 - Shed Roof: We're building a shed with a roof having the same slope (a 2" pitch) as our mudroom, to run 12 feet out into the yard with its end wall 6 feet tall. How far up the mud room wall will the shed roof need to be attached? If roof line of the mudroom is 12'6" off the ground and we just continue the roof of the shed from the roof of the mud room, how far out into the yard would it go before it was 8 feet off the ground?
January 29-February 2 - Superbowl Sunday: It's Superbowl Sunday and the Steelers are losing 20-17. They have a chance to tie the football game with a field goal (worth three points) from 50 yards away. If the kicker is on a direct line to the goal posts, how far off that line could the ball be when it crosses the line of scrimmage and still go through the goal posts? How far does the kicker have to kick it to get it over the cross bar?
February 5-9 - Felling a Tree: I need to cut down a tree that's shading my garden and drop it between the garden and another tree; if it's taller than 59 feet it will smash my lilac bush. I measured the tree's shadow and my shadow standing next to it - the tree's shadow was 76'8", and mine was 94 inches. I'm 5'10"; will the tree land on the lilac?
February 12-16 - Women's Basketball: Let's say that the average men's college basketball player is 6'3", and the average woman is 5'6". The court is about 78 feet long, the basket is 10 feet high, the free-throw line is 15 feet from the basket, the 3-point line is 19 feet from the basket, and the hoop itself is 18" in diameter. How would we need to scale the court down to make the women's game like the men's?
February 19-23 - Construct Segment EF: Given an angle ABC, and any point D in the interior of angle ABC, construct a segment EF such that D is the midpoint of segment EF, E lies on ray BA, and F lies on ray BC.
February 26-March 1 - Stringer Angles: At what angle should my stringers (supports) meet the top board of my new steps? If I cut them at 90 degrees, they won't lie flat against the header.
March 4-8 - Areas of Squares: Given two squares and a circle, one square having the diameter of the circle as an edge and the other square inscribed in the circle, what is the area of the small square compared to the area of the larger square?
March 11-15 - Quilting: How much fabric will I need to make a queen-size quilt using a pattern called "The Mariner's Compass"?
March 18-22 - Circumscribing a Polygon: Given a circle with any chord drawn, prove that the perpendicular bisector of the chord goes through the center of the circle. Given any polygon, explain how to decide whether you can circumscribe a circle around it.
March 25-29 - Pythagorean Theorem: One very familiar proof is a right triangle with squares on each side. Do we have to use squares? What about hexagons, or other shapes? Why do you suppose squares are usually used for this proof? Extra: What U.S. President discovered a proof of the Pythagorean Theorem?
April 1-5 - Overlapping Squares: Two congruent 8 cm x 8 cm squares overlap. A vertex of one square is at the center of the other square. What is the largest possible value for the area where they overlap?
April 8-12 - Triangle ABC with area 20: Given: A(0,6), B(0,10), C(x,y), and the area of triangle ABC is 20. 1) If triangle ABC is isosceles, find C(x,y). 2) Find all points C(x,y) such that the area of triangle ABC is 20.
April 15-19 - Construct an Isosceles Triangle: Give at least three different ways to construct an isosceles triangle (a construction can be repeated over and over and in this case will always yield an isosceles triangle).
April 22-26 - What Path?: If I follow a path so that my lines of sight back to a dock and to a bridge up the shore are always perpendicular, what sort of path will I travel?
April 29-May 3 - What's the best angle?: One person says that the best place to sit at a baseball game is where your lines of sight between home plate and first base meet at a 25-degree angle, and that there is one seat where this is true. Another person agrees about the 25 degrees, but feels that there are more places where you could sit. Who is right?
May 6-10 - Earthquake: The epicenter of an earthquake is 6.3 miles ENE of Duval, Washington (USA). Steve lives 7 miles ENE of Duval. The earthquake happens 5 miles underground (under the epicenter - the "epicenter" is the place on the surface directly above the earthquake). How far is Steve's house from the epicenter, and how far is his house from the actual location of the earthquake?
May 13-17 - Postage Stamps: Fold a block of eight postage stamps, along the perforations and without tearing, so as to form a single pile with the stamps numbered consecutively from top to bottom.
May 20-24 - How long is the belt?: The diameters of two wheels are 18 cm and 12 cm and their centers are 30 cm apart. A belt goes around them and crosses 18 cm from the center of the big wheel. How long is the belt? How do you know you're right?
May 27-31 - Great Circles, Nautical Miles: The great circle around Earth's equator has a radius of 6378 kilometers. The great circle around the poles has a radius of 6357 kilometers. What would a nautical mile (the length of one minute of arc of the great circle) be for each of these circles? Do you think the agreed-upon distance of 1.852 kilometers per nautical mile is a good compromise?
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