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Mathematical science fair projects for school! |
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Draw A Right Triangle With A Cool Acute Angle!
Congruent triangles form an isometry. And triangles are studied in geometry. And triangles can also be the focal point of your cool mathematical science fair projects!
Right triangles, which contain right angles, are indispensable in such fields as astronomy, electrical science and engineering. A very important right triangle, that 5th, 6th and 7th grade middle school students encounter every day, is a right triangle with a pair of equal sides. An amazingly clever idea for a science fair math project is to illustrate the proof of a hypothesis (or theorem) about the area of triangles. For this particular middle school or high school math science project, we will limit our attention to right triangles with a pair of equal sides. The formula that we will use in our mathematical science fair projects is the formula for the area A of a triangle with base b and height h, which is A = (1/2)*b*h . It is fascinating that this formula, which is understood by even some 4th grade students, also has wide spread applications in science research! We will now do a descriptive experiment to illustrate that the formula is true! We will now give the step by step instructions for this exciting sure to win project that will also help to improve your grade in science and math! But first note that a T-Square will be very useful in these Mathematical science fair projects. a) On a 22 x 28 (inch) white poster board, using a T-square and ruler, draw a sequence of parallel horizontal lines that are also parallel to the base. The lines are to be spaced one inch apart. The bottom line is to be one inch above the base and the top line one inch below the top edge. Now in a similar fashion b) draw a sequence of parallel vertical lines that are also parallel to the sides. The lines are to be spaced one inch apart. Please note: you may use metric units or conventional units in these Mathematical science fair projects. The vertical line on the extreme left will be one inch from the left side of the poster. And the vertical line on the extreme right will be one inch from the right side. Your poster board now is filled with a grid of one inch squares! Such a grid can be used for a variety of cool science project ideas! Now you want to draw a right triangle with equal sides on it. As you will recall from your middle (or high) school math classes, a triangle has three vertexes. It will be convenient to designate these vertexes, in your Mathematical science fair projects, as P, Q and R. Now c) let P be a grid point near the bottom left of your poster: and let Q be a grid point on the same horizontal line as P but located 12 inches to the right of P. Now let R be a grid point that is 12 inches directly above Q. You now have the vertexes of a right triangle PQR! Use your marker to connect the vertexes of this triangle with bold lines. You are now almost ready to perform some very clever, descriptive and informative experiments! These will make your mathematical and science fair projects surefire winners! Your display boards will feature the simplification of an important math principle so that even elementary school kids can understand it! The base b and the height h of this triangle are given by b =12 and h = 12. Substituting these values into the formula for the area A results in A = 72 (square inches). Now we will determine that same area using a fun science fair mathematical experiment: d) count the number of Complete Squares in the triangle PQR; let C denote this number. Now e) count the number of "Half Squares" that lie directly under the hypotenuse of the right triangle PQR, of your mathematical science fair projects. Let H denote this number. The next step is to f) let B = C + (1/2)*H. Now substitute the values of C and H, obtained from the counting, into this formula. Note that A and B are the same! The topic of an optional exciting science fair mathlete challenge would be to explain why! Or you could leave that for your next set of cool mathematical science fair projects! For this project you will only need poster boards, display boards, T-Square, meter stick (ruler), markers and a calculator.
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