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=Quaternions: History= | =Quaternions: History= | ||
| + | Every professional wishes to have that one monumental light bulb moment in his or her life. That split second when an academic is stuck on a problem but has a sudden insight that launches him/her into fame. Perhaps such epiphanies and light bulb moments are more dramatized by films and are less common in real life. But the discovery or perhaps the development of quaternions has a remarkable light bulb moment and a thrilling story that almost sounds like the plot of a movie. | ||
| + | An Irish man in the 1840s named William Rowan Hamilton wanted to extend the complex number system to a higher dimension. Hamilton was aware of complex numbers and the fact that you can use complex numbers to model a rotation in two dimensions using Euler’s Formula. Hamilton was also aware of the work of Olinde Rodrigues, another mathematician who worked on transformation groups. | ||
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| + | But Hamilton had much trouble extending the complex system to three dimensions. In one of his books Hamilton wrote how his brother would always ask him every morning, "Well, Papa, can you multiply triples?" But he always had a pessimistic reply, "No, I can only add and subtract them." | ||
| + | Later that year, Hamilton and his better half were taking a walk along the Royal Canal in Dublin. As they were walking across a bridge, the answer to the puzzle suddenly came to Hamilton. He has his light bulb moment just like the movies. He realized that one could not perhaps easily multiply or divide triples, but he could do so with quadruples. He realized he could use 3 of the numbers in the quadruple to specify a specific point, further validating his system. Just when Hamilton was struck with this sudden knowledge, he grabbed a rock near him on the bridge and carved on it the multiplication identity that allows quaternion multiplication. | ||
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| + | To this day one can visit Ireland and see the rock on the bridge where quaternions were born. In fact, in Hamilton’s honor there is a parade every year through the bridge on October 16. | ||
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| + | Quaternions were a hot topic in the 1840s when Hamilton discovered them. But for the next 150 years they were mostly a mathematical curiosity. It was not until the late 20th century that we found widespread applied uses of Quaternions. Hence, it would not be a stretch to say that quaternions is a field of mathematics that has had a recent rebirth. | ||
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| + | https://en.wikipedia.org/wiki/History_of_quaternions | ||
| + | https://www.google.com/search?q=hamilton+rock+quaternion&safe=active&rlz=1C1ZKTG_enUS917US917&sxsrf=ALeKk00eSUXBwvdR_ieT1AKk3K-R94kwrg:1606758604159&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjNrdye6qrtAhUMQ80KHZ-HAZoQ_AUoAXoECAcQAw&biw=1536&bih=722&dpr=1.25#imgrc=hi3zU59fNKnfiM | ||
| + | |||
| + | https://www.maa.org/sites/default/files/images/images/upload_library/46/HOMSIGMAA/Buchmann.pdf | ||
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Latest revision as of 13:09, 30 November 2020
Quaternions: History
Every professional wishes to have that one monumental light bulb moment in his or her life. That split second when an academic is stuck on a problem but has a sudden insight that launches him/her into fame. Perhaps such epiphanies and light bulb moments are more dramatized by films and are less common in real life. But the discovery or perhaps the development of quaternions has a remarkable light bulb moment and a thrilling story that almost sounds like the plot of a movie.
An Irish man in the 1840s named William Rowan Hamilton wanted to extend the complex number system to a higher dimension. Hamilton was aware of complex numbers and the fact that you can use complex numbers to model a rotation in two dimensions using Euler’s Formula. Hamilton was also aware of the work of Olinde Rodrigues, another mathematician who worked on transformation groups.
But Hamilton had much trouble extending the complex system to three dimensions. In one of his books Hamilton wrote how his brother would always ask him every morning, "Well, Papa, can you multiply triples?" But he always had a pessimistic reply, "No, I can only add and subtract them." Later that year, Hamilton and his better half were taking a walk along the Royal Canal in Dublin. As they were walking across a bridge, the answer to the puzzle suddenly came to Hamilton. He has his light bulb moment just like the movies. He realized that one could not perhaps easily multiply or divide triples, but he could do so with quadruples. He realized he could use 3 of the numbers in the quadruple to specify a specific point, further validating his system. Just when Hamilton was struck with this sudden knowledge, he grabbed a rock near him on the bridge and carved on it the multiplication identity that allows quaternion multiplication.
To this day one can visit Ireland and see the rock on the bridge where quaternions were born. In fact, in Hamilton’s honor there is a parade every year through the bridge on October 16.
Quaternions were a hot topic in the 1840s when Hamilton discovered them. But for the next 150 years they were mostly a mathematical curiosity. It was not until the late 20th century that we found widespread applied uses of Quaternions. Hence, it would not be a stretch to say that quaternions is a field of mathematics that has had a recent rebirth.
https://en.wikipedia.org/wiki/History_of_quaternions https://www.google.com/search?q=hamilton+rock+quaternion&safe=active&rlz=1C1ZKTG_enUS917US917&sxsrf=ALeKk00eSUXBwvdR_ieT1AKk3K-R94kwrg:1606758604159&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjNrdye6qrtAhUMQ80KHZ-HAZoQ_AUoAXoECAcQAw&biw=1536&bih=722&dpr=1.25#imgrc=hi3zU59fNKnfiM
https://www.maa.org/sites/default/files/images/images/upload_library/46/HOMSIGMAA/Buchmann.pdf
