20Apr 2017 by Vincent Summers 2 Comments

Cuprous Sulfate: A Disagreement with My High School Chemistry Teacher

Chemistry, Education
[caption id="attachment_17698" align="alignright" width="440"] Classroom[/caption] As a kid, I was excessively shy and retiring – except when it came to matters of science and math. When it came to them, I was generally quiet but I could become quite outspoken if the occasion arose. During senior year, I approached my math instructor and told him an entire chapter in our textbook was wrong. He was reluctant to hear me out, but when he did, he acknowledged I was correct. On one occasion during junior year, I was listening to my chemistry teacher attentively when he spoke of cuprous sulfate. For those who are unacquainted with terminology, this would have been the old name (the name I still use) for copper(I) sulfate. I informed Mr. D’Alesandro that the only existing copper…
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18Apr 2016 by Vincent Summers 3 Comments

Parametric Equations: I Corrected the Text Book

Education, Mathematics
A former fellow high school student, Ted L., recently contacted me. He wrote concerning our senior year, in which we shared a math course that included parametric equations. Ted Talks “I recall being in the advanced math class with Mr. Miller where I struggled quite a bit. In a discussion about solving some problem, you presented an alternative solution. Mr. Miller quickly dismissed your idea in a rather condescending fashion, shaking his head and stating, "No Summers, [you’re wrong]," with a tone that suggested your idea was rather silly, perhaps bordering on absurd. But you persisted, in a back and forth between you, that lasted for several minutes. During that discussion, I was completely lost, having no idea at all what either of you was talking about. After many gives…
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24Jul 2015 by Vincent Summers No Comments

Mathematical Equation for a Cone

Mathematics
You go to the mall and request a double scoop of Rocky Road ice cream. The fellow serving says "Yes," and then he asks you asks if you would like that on a wafer or a sugar cone? Since most have eaten ice cream since childhood (unless we are dairy or otherwise intolerant), the majority of people think of a simple v-shape hollow structure as a cone. It has a top. It has a bottom. But is this the kind of geometrical shape that mathematicians think of when they refer to deriving the mathematical equation of a cone? A Mathematics Cone The cone of the mathematician bears some resemblance to that, but there are differences. The figure included with this article demonstrates that there are two v-shaped portions, not one.…
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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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04Mar 2014 by Vincent Summers 2 Comments

Sample High School Math Problems with Answers

Mathematics
[caption id="attachment_5578" align="alignright" width="440"] Fractal - CCA Share Alike 3.0 Unported by Wolfgang Beyer[/caption] Want some sample high school math problems with answers? Well then here you go! High School Math Problems Problem 1:     A change purse has 100 nickels and dimes. The total value of the coins is $7. How many coins of each type does the purse contain? If the number of nickels is N and the number of dimes is D, then 5N + 10D = 700 (the 5, 10 and 700 representing the number of cents) However, N + D = 100 (the number of nickels plus the number of dimes equals 100) So, solving for N for both equations, we get as the result N = – 2D + 140 and N = 100 – D…
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