Math - Dot paper drawings

Math - Dot paper drawings - back to our starting side, and...

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1. 3. Obviously if you wind up facing in the same direction at the end that you were in the beginning the total of your angles, countinf one direction as positivr and the other as negative must be a multiple of 360 degrees. Think of a rectangular flag and cut out a 45-45-90 right triangle with hypotenuse corresponding to one of the width, Starting at the oppositie width we go 90 deg + 135 deg - 90 deg + 135 deg + 90 deg at which point we are facing the same direction again along th opposite width--and our total is 360 deg. Now cut out 45-45-90 right triangles along the rectangle's width on both sides. Starting with s length we go 135 deg - 90 deg + 135 deg + 135 deg - 90 deg + 135 deg which brings us
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Unformatted text preview: back to our starting side, and the total is again 360 deg. This time cut the triangle out of the first width side, and attach it to the opposite side width. Starting with a length facing the first side width we get 135 deg - 90 deg + 135 deg + 45 deg + 90 deg + 45 deg at which point you are back to the original side and your total is again 360 deg. Just to make the situation clear, if you go around a stop sign(a regular ocatagon) each of the octagon's interior angles will be 135 deg--but the turns are all 45 deg turns in the sense that the change in direction is 45 deg. The change of direction angles are the ones we are adding to get 360 deg in these problems....
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Math - Dot paper drawings - back to our starting side, and...

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