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1700 BCE
Babylonian Clay Math
It is estimated and theorized that even before the Greeks discovered irrational numbers, the Babylonians were already using clay tablets that approximated the square root of 2. Why did it take 1,200 later to rediscover this? -
1650 BCE
Egyptian Method for Irrational Numbers
The Rhind Papyrus demonstrated an example of when the Egyptians extracted the square root of numbers using the inverse proportion method. -
650 BCE
Ancient Indian Aryabhata approximated the square root of 2
Ancient Indian Aryabhata had a very close approximation of the square root of two and three,which gives us a good method for finding the square root of numbers with many digits. -
520 BCE
The Dangerous Ratio
Pythagoras' student, Hippassus discovered a mathematical secret of the square root of 2. However, the Pythagoreans were upset and jealous and dubbed this number to be incommensurable. The positive in the situation was the discovery of irrational numbers, but the down side is that supposedly Hippassus suffered a tragic loss. These speculations continue a on for many centuries. -
400 BCE
Who discovered it first?
Plato describes Theodorus of Cyrene, in his book Theaetetus, to have possibly discover irrational numbers up to the square root of 17 before any other mathematicians. -
900
Abu Kamil worked with irrational numbers
Abu Kamil worked with roots of rational numbers, or "surds" in algebraic equations. -
1000
The book about the Pythagorean's "irrationality"
According to "Math Through the Ages" Abu Bakr al-Karaji wrote in his book about algebra and arithmetic that focused on the Greeks geometric irrationals could be treated as numbers. -
1100
Bhaskara II describes rules for square roots
The Indian, Bhaskara II, describes rules for completing the calculation of square roots and non-square root integers. -
1300
News of Math to Europe
A few years later, the mathematics was analyzed and shared with the Europeans. They engaged in discussions with the Arabic culture about topics in math and then studied about Greek mathematics, as well. -
Stevin declared that rational and irrational numbers are alike.
Flemish mathematician, Simon Stevin, wrote in his book the Tenth that rational and irrational numbers are similar and both worthy of being called numbers. He later demonstrated his idea on the number line. Thank you Stevin for this life changing LESSON. -
A Suppressed Advance
A few years later, a French philosopher, Rene Descartes, described a coordinate plane in his text, La Geometrie, and failed to use irrational numbers. He ignored the idea and mentioned that it was irrelevant for his work and only needed "real numbers", because they corresponded with his work. -
e (Uler) Irrational Find - e - ngs.
As time continues to pass, the history of rational and irrational numbers is ever changing. Swiss mathematician, Leonhard Euler, introduced the letter e as a base for logarithms, and shares his finding in "Mechanica". The e became a standard, and ever so famous, irrational number also known as Euler's number. -
Let's Celebrate with Pi(e)
Later on Descartes realized the use of irrational and rational numbers in calculus. A few centuries later, Johann Lambert, Swiss mathematician, proved that pi was irrational. -
To Exist or Not Exist that is the Question?
Leopold Kronecker expressed that irrational numbers do not exist. This on going argument is debated and eventually was settled by a few mathematicians, and even more were trying to find the decimal points for irrational numbers, especially pi. -
Transcendentalist Numbers
After some time, irrational numbers received a different name, transcendental, by English mathematician, John Wallis. However, later on, Joseph Liouville, French mathematician. His number theory demonstrated that every rational number can be proven and irrational numbers, Liouville number can not be proven. Some examples include 1!, 2!, 3!, etc. -
Cantor and Cauchy
Now, rational and irrational numbers are considered real numbers, but it may be hard to show this if the irrational number on the number line. We llearned that if a decimal has a repeating pattern, it is rational and if it had an infinite amount of decimals it would be irrational. Cantor posted his finding in a paper and provided a model to represent his idea for rational and irrational numbers, but later Cauchy described this sequence which became known as Cauchy sequence. -
Challenge Accepted
French mathematician, Charles Hermite, took on the challenge of proving that e^r was transcedental for all rational numbers r, and succeeded. However, when trying to solve that pi was transcendental, was not as easy as an endevour. -
The Number Line Continuum
After many teachers and students in the 18th and 19th century continue to work with irrational numbers, like Cauchy and Dedekind, another mathematician Cantor, started to see a pattern for numbers on the number line. He was building of the work of K. Weierstrass and figured out that the sequence on the number line can place decimals and fractions in a sequence without limitation, rational or irrational. -
Challenge Completed
Meanwhile, nine years later, German mathematician Ferdinand Lindemann, proved that pi is a transcendental number. He is renowned for his finding. According to Lindemann, the proof of pi is transcendental. -
Hilbert's Challenge
David Hilbert had a 23 problem challenge, which he mentioned to the Second International Congress of Mathematics. This sparked interest for mathematicians where Gelfond and Schneider proved
these problems and that all such numbers are transcendental including 2 to the square root of 3 and other algebraic and algebraic irrational numbers. -
Pi Computation
Over time, the irrational number pi was computed by many, but not until recently did we find the most digits by Peter Trueb. It took him 105 days to do the computation and he computed it to have 22,459,157,718,361 digits. This calculation of pi(e) happened just in time for the Thanksgiving.
