7/7/2023 0 Comments Rotating 4d sphere![]() ![]() Which today bears a plaque in his honor showing that equation. ![]() He carved the crucial equation describing these three imaginary units into theīridge. And the real numbers sitting perpendicular to that in some kind of fourthĭimension. Three imaginary dimensions describing space. But to add two more imaginary dimensions. With a supposed flash of insight, that what he needed was not to add a singleĭimension to the complex numbers. And, as the story goes, his son would ask him every morning whether or not he hadįigured out how to divide triples and he would always say, “no, not yet.” But on October 16th, 1843, while crossing the Broome Bridge in Dublin, he realized, Three-dimensional number system analogous to the complex numbers. The Irish mathematician William Rowan Hamilton spent much of his life seeking a The story of their discovery is also quite famous in math. They have a surprisingly pragmatic utility for describing rotation in threeĭimensions and even for quantum mechanics. But they’re not just playful mathematical shenanigans. Quaternions are a four-dimensional extension of complex numbers. Just as complex numbers are a two-dimensional extension of the real numbers, Quaternions are an absolutely fascinating and often underappreciated number systemįrom math. One which you’ll understand by the end of this video. On a four-dimensional sphere being represented in our three-dimensional space. ![]() Or rather, you’re looking at a certain representation of a specific motion happening What you’re looking at right now is something called quaternion multiplication. ![]()
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