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)”

Liar, Lunatic, or Lord?: Overview of Lewis’ Famous Argument

CS Lewis is perhaps the most recognized Christian writer of the twentieth century. From the well-known and loved Narnia books to the more theological and apologetics books like Mere Christianity and The Screwtape Letters, Lewis has captured both the imagination and intellect of his many readers since he began his writing. CS Lewis’ analogies, argumentsContinue reading “Liar, Lunatic, or Lord?: Overview of Lewis’ Famous Argument”

Antiderivatives (Explaining Calculus #15)

In the last post in the series on calculus, we talked about Riemann sums – which is just a fancy way of speaking of estimating the area of a complicated region by using lots of rectangles to obtain an approximately correct answer. The post that I must follow this up with, which for now seemsContinue reading “Antiderivatives (Explaining Calculus #15)”

The Natural Numbers and Zero (Types of Numbers #2)

I now begin the escapade into different sorts of numbers. This may seem rather a strange adventure to anyone who hasn’t listened to too many professional mathematicians talks, or anyone who is too far removed from high school education. I would guess that most people who have read this have some particular picture of numberContinue reading “The Natural Numbers and Zero (Types of Numbers #2)”

The Kalam Cosmological Argument: A Brief Overview

In a previous post, I have discussed the intuition behind cosmological arguments and gave several examples. One of these examples was the Kalam cosmological argument. By way of overview, a cosmological argument is, broadly speaking, one that reasons from facts about the universe we observe and metaphysical principles to argue that God, or at leastContinue reading “The Kalam Cosmological Argument: A Brief Overview”

Riemann Sums and Areas (Explaining Calculus #14)

At this point in calculus, we are taking what appears to be a sharp turn in a direction completely away from what we’ve been doing so far. We now turn to talking about areas. The Problem Geometry is one of the most important branches of all mathematics, both theoretical mathematics and applied mathematics. When middleContinue reading “Riemann Sums and Areas (Explaining Calculus #14)”

What are Cosmological Arguments?

Cosmological arguments are probably the most discussed and most intriguing area of natural theology. While there are a great variety of areas of philosophy that point towards God’s existence – we find that, for whatever reason, the realm of cosmological arguments seems to bring the most interest from both defenders and opponents of the arguments.Continue reading “What are Cosmological Arguments?”

Critical Thinking Toolkit: Straw Man Fallacy

Imagine the following scenario. A man walks up to an 80 year old with walking on his cane in the street, knocks him out with a single punch, then claims to be the best boxer who has ever lived. Sound silly? It should. This is an embodiment of what is known as the straw manContinue reading “Critical Thinking Toolkit: Straw Man Fallacy”