The Greeks took their mathematics seriously…were they perhaps “deadly serious”?

Geek Irony Stemming from the Square Root of Two

Yesterday Decoded Science published “The Square Root of Two is a Real Irrational Number“. This article is a follow-up to “Cantor Defeated Galileo in the Battle of Infinite Numbers“, where I casually mentioned the square root of 2 but did not prove my statement.

Pythagoras believed that only rational numbers existed, and could handle any situation. However, his “very own” Pythagorean Theorem led to the proof that the square root of two is irrational; it cannot be expressed as a “ratio” of two integers. Euclid, however, devoted Book X of his multi-volume “Elements” to finding both rational and irrational numbers, so he was cool with the concept.

As always, I also promoted this article in my Blog of Writing. “Preview of the Irrational Square Root of Two” includes a writing tip about creating images, especially from spreadsheet programs.
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By the way, another Blog of Writing article, “The Fall 2011 Insect Pest Collection” has a good a writing tip about fatigue!

Professional Writing by DeHaan Services

DeHaan Services writes web site content or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, and other web sites. That’s why we highlight articles on this blog page.

To only see our Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the left-hand margin.

Thank you for reading about the ancient Greek problems regarding the irrational square root of two.

Surprisingly, infinity comes in a variety of sizes.

Battle of the Infinite Sets: Galileo versus Cantor

My recent Decoded Science article, “Cantor Defeated Galileo in the Battle of Infinite Numbers“, explains how Cantor proved that not all infinities are created equal.

Here  are some questions: are there more fractions than integers? More real numbers than fractions? Could you set up a system to count the rational numbers?

As usual in my “Mathematics” articles, my Decoded Science story includes a brief biography of Georg Cantor.
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Added Publicity for Cantor’s Infinities in my Blog of Writing

As always, I also publicize my articles in my Blog of Writing. “Preview of the Infinite Real Numbers of Cantor” includes a writing tip as a bonus feature.

Professional Writing by DeHaan Services

DeHaan Services writes web site content or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, and other online sites. That’s why we highlight articles on this blog page.

To only see our Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the left-hand margin.

Thank you for reading about the battle between Galileo and Cantor for the larger infinity.

Why would an Italian astronomer want an infinite set? What paradox did Galileo exploit?

What did Galileo do with Infinite Sets and Paradoxes?

Galileo Galilei, the famous Italian astronomer, wrote a book in which he tried to prove that a long line segment and a short line segment had the same “number” of points, even though one was obviously longer than the other.

How did Galileo demonstrate his paradox? Is it a convincing argument, or did he slip up with his infinite sets?

My article, “The Paradox of the Infinite Series of Squares Numbers by Galileo” in Decoded Science, explains how Galileo presented this charming paradox.

As always, I also publicized this article in my Blog of Writing, where “Preview of Galileo and his Paradox of Squares” includes the preview of images I made for the article as well as my “writing tip”
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Professional Writing by DeHaan Services

DeHaan Services writes web site content or advertising copy for clients. Our skills are demonstrated in articles in Decoded Science, and other online sites. That’s why we highlight articles on this blog page.

To only see our Toronto events or fitness, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Thank you for reading about Galileo’s paradox of infinite sets.