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Rational numbers can be expressed as the ratio of two integers, while irrational numbers, such as square roots of non-square numbers, cannot.
Because every transcendental number is irrational, any proof showing that pi is transcendental also proves that pi is irrational.
Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational ...
Here are some nerdy facts about the irrational number, to impress your friends as you celebrate Pi Day (which is also Albert Einstein's birthday). [The 9 Most Massive Numbers in Existence] 1.
The number π is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's an irrational number, meaning that it can't be represented by a common fraction.
Is π really irrational? Yes, really really. It is completely, unequivocally and blatantly not a rational number. The interesting question for me, and one I've accepted I'll never know the answer ...
Test yourself on math's most famous constant with this pi quiz.