I'm always on the lookout for ways of visualizing mathematical results. In this essay I'm going to restrict myself to pictures. Furthermore, I'm going to...
For quite a while, I knew of only one proof of the "infinitude of primes", namely Euclid's proof. Over the years, I've come across others, and I've noticed...
The Fibonacci essay I mentioned a few days ago is done. There's now roughly twice the content than there was in the original incomplete version. As before,...
Properties of Fibonacci numbers are often proved by induction. Although this results in technically correct proofs, I find that proofs by induction usually...
Hello, I'm new to the group. I'm trying to get my brain wrapped around the concept of a Googleplex. I *think* * understand a Google. It's one followed by 100...
Hello, I'm new to the group. I'm trying to get my brain wrapped around the concept of a Googleplex. I *think* * understand a Google. It's one followed by 100...
... Hard to say. The arithmetic follows from known algebraic identities. That part of your findings isn't new. As for the historical/biblical connections, I...
I was wondering. Yes, I was wondering this morning about some basic arithmetic, I have pompously titled, the S.S. Code, (the reason for such could be given in...
The identity 3*5=15 quickly leads to more mathematics: various algebraic identities, an infinite product, Fibonacci numbers, the Golden Ratio, Mersenne primes,...
I've posted a new essay on "Large Numbers". It's at <http://www.gbbservices.com/math/large.html>. "This is about some ways I've come up with to get a gut ...
I've posted a new essay on "Solving The Cubic". It's at <http://www.gbbservices.com/math/cubic.html> Hope you enjoy it, Walter P.S. I know that some of the...
My book claims that, ... So, this just means that |x| breaks into two equations, x => 0 -x < 0 But, I am not clear how my book jumps from this to saying that x...
Hi Corey, ... Wow, this is hard to answer, especially via email! It seems to me that you really want to clarify just what you're given, and what you have to...
Hello Group, Let D represent capital Delta and denote the symmetric difference of two sets A and B. Prove that, (A D B) is logically equivelant to (A union B)...
It occurred to me that in all the discussion about Pythagoras' identity, and its generalization to general triangles, the actual generalization (called the law...
Hi Corey, It's "Dedekind". He was a German mathematician: Julius Wilhelm Richard Dedekind. If you search on "Dedekind cut" you'll find lots of references. In...
... I thought about it last night, and came up with something that might help. Given an a,b,h triangle, we know that h is a function of a and b, i.e. h=F(a,b)....
Hello group, I'm trying to learn about something called, and please correct my spelling, "Dedican Cut arithmetic". Does anyone know what it is? I'm reading a...
Hi Dave, ... There's a multitude of proofs of Pythagoras' theorem! Even President Garfield got into the act and provided a proof in 1876. To answer your...
Hi Walter, This is Dave C. of the StonyBrook Aquatic team. I was looking at you connections on Pythagoras. Although I know how to "prove" a^2 + b^2= h^2 for...
... Sure, I'll give it a go. There's lots of ways to do it. Here's the most direct one I can think of: Assume the conclusion is false. That means, assume it is...
Hello Everyone, Given that -a < 0, prove that a > 0 by assuming the conclusion is false and prove that it must be the case by contradiction. I was not exactly...
Conservation of Energy gives yet another interpretation of the trigonometric identity cos^2(t)+sin^2(t)=1. I've updated the essay on this identity. Just follow...
My first essay is now online. You'll find a link at http://www.gbbservices.com/mathematics.html The essay revisits the trigonometric identity cos^2 + sin^2 = 1...
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