The Pythagorean Belief in Rational Numbers

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Now, if you don’t know what I’m talking about, let me explain: the Pythagoreans were ancient Greek mathematicians who believed that all numbers could be expressed as ratios of whole numbers (i.e., integers).

Now, this might sound like a pretty reasonable idea at first glance after all, we use fractions and decimals in our everyday lives to represent quantities that can’t easily be measured with whole numbers. But the Pythagoreans took it one step further: they believed that these rational numbers were not just useful for practical purposes, but also had some sort of mystical significance.

According to legend, a young man named Hippasus discovered that there was no way to express certain irrational numbers (like the square root of 2) as ratios of whole numbers. This discovery caused quite a stir among the Pythagoreans they were so upset by it that some even went so far as to kill him for his heresy!

Now, I know what you’re thinking: “Wait a minute, why would anyone get so worked up over something like this?” Well, let me tell you the Pythagoreans believed that everything in the universe could be expressed as ratios of whole numbers. They thought that these ratios were somehow connected to the divine order of things and that by understanding them, they could unlock the secrets of the cosmos.

Of course, we now know that this is not entirely true there are plenty of irrational numbers out there (like pi or e) that cannot be expressed as ratios of whole numbers. But at the time, the Pythagoreans were convinced that their belief in rational numbers was the key to unlocking the mysteries of the universe.

So, if you ever find yourself struggling with a math problem and feeling frustrated by all those ***** irrational numbers, just remember: the Pythagoreans believed that everything has its own unique ratio even if we can’t always see it at first glance!

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