Welcome to the blog! You’ll see some of my most recent posts here. I write about mathematics, theology, apologetics, philosophy, and any variety of related topics. If you are interested in my mathematical work, click here to see my academic website.
Why Prove a Theorem Twice?
I have written before on the problem and solution of the problem of “Pythagorean Triples”. The problem, based on the Pythagorean theorem for right triangles, asks for all possible solutions to this equation which have all of whole numbers. Not just any right triangle works – for instance if then , which is definitely notContinue reading “Why Prove a Theorem Twice?”
The Realm of Integers (Types of Numbers #3)
To kick off the tower of numbers, so to speak, the last article in this series discussed the “basic” numbers – mainly focusing on the positive whole numbers but also including zero. Now, we haven’t quite explored every aspect of the number zero yet, and we ran into problems with subtraction within the so-called “naturalContinue reading “The Realm of Integers (Types of Numbers #3)”
Fundamental Theorem of Calculus, Part 1 (Explaining Calculus #16)
We have recently talked about two concepts that appear rather disparate. We have discussed antiderivatives – which is the idea of reversing all the rules for taking derivatives, and Riemann sums, which are used to calculate the areas underneath complicated shapes. What do these have to do with each other? It does not look likeContinue reading “Fundamental Theorem of Calculus, Part 1 (Explaining Calculus #16)”
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