29Sep 2015 by Vincent Summers No Comments

Collapsing then Expanding the Equation for a Sphere

Mathematics
[caption id="attachment_8626" align="alignright" width="480"] How simple is a sphere?[/caption] Equation for the Simplest Sphere The equation for a sphere with its center at the origin is: x2 + y2 + z2 = c2 Where c is a positive constant. For simplicity, let's choose a positive constant, k, such that k = c2. Equation for a Circle by Collapsing a Sphere Collapsing it in one dimension generates the equation of one of three circles: x2 + y2 = k x2 + z2 = k y2 + z2 = k Equation for a Point by Collapsing a Circle Collapsing the three circles in one dimension generates two equations representing precisely two points for each of them: For x2 + y2 = k, x²2 = k y2 = k For x2 + z2…
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07Mar 2014 by Vincent Summers No Comments

Secondary School Math Problems Plus Solutions

Mathematics
[caption id="attachment_5613" align="alignright" width="480"] Fractal[/caption] For some, it's actually fun when they come across secondary school math problems plus solutions. It's because they are no longer accountable, since they graduated years ago. Math Problems Plus Solutions Problem 1: Find the slope intercept form of the line passing through the point (– 1, 5) and parallel to the line – 6x – 7y = – 3. The line given is rewritten (in slope-intercept form, y = mx + b) as y = – 6/7 x + 3/7 Thus the slope m = – 6/7 Now two lines are parallel if they have the same slope. So, y = – 6/7 x + b is the formula for the new line, with the intercept not yet solved. We do so by inserting…
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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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