31Jul 2015 by Vincent Summers No Comments

Generate 2D Math Objects by Collapsing 3D Math Objects

Mathematics
I had some excellent high school mathematics instructors. They both loved their field and took an interest in their students. Since high school, I have had a deep interest in collapsing 3D mathematical equations to derive equations for 2D mathematical objects or modifying 2D objects into other 2D, or 2D objects into 1D. A 3D sphere becomes a 2D circle. A 2D parabola becomes a 1D line. The 2D hyperbola shown, if collapsed along the x-axis, becomes two 1D line segments stretching at one end to infinity. The same hyperbola collapsed along the y-axis becomes a complete line. A 2D circle becomes a single 1D line segment of a length equal to the diameter. An Example of Collapsing 3D into 2D What can be obtained by collapsing 3D math objects…
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07Mar 2014 by Vincent Summers No Comments

Eight Middle and High School Math Problems with Solutions

Mathematics
Not only current students. but old-timers as well will find these middle and high school math problems informative. Middle and High School Math Problem 1: Leaves from a tree were reported by four different European students to be 2.9 cm, 3.33 cm, 3.9 cm, and 3.12 cm in length. List the numbers in order of decreasing length. For the beginner, the easiest way to evaluate which of these number is smaller and which is larger, is to make the number of digits to the right of the decimal the same. Now the maximum number of such digits here is two. Adding zeros to the right of the last digit does not change a number’s value. When that is done, the numbers become: 2.90, 3.33, 3.90 and 3.12 In decreasing order,…
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