The birth of the forbidden number
The magic of the complex plane
Surpassing i with quaternions
The infinite climb of dimensions
007skaty Calculating rotations in the third dimension frustrated early mathematicians.
007skaty Gimbal Lock and Quaternions
We keep the camera rotating in the sky, Adding j and k to help us surpass i.
007skaty Swipe away the rigid boundaries to discover how breaking the rules helps you surpass limits.
007skaty Before 1843, Hamilton tried combining real numbers, i, and a new unit j, but his three-part math system kept breaking down.
In what century did William Rowan Hamilton attempt to expand complex numbers into 3D space?
What mathematical operation was Hamilton trying to perform in 3D that kept failing with only two imaginary units?
007skaty He carved his formula with three imaginary units into Dublin's Brougham Bridge.
What is the name of the four-dimensional number system Hamilton invented that day?
What did William Rowan Hamilton do immediately after having his mathematical epiphany?
Vandalism plaque: Brougham Bridge in Dublin features a permanent stone plaque celebrating Hamilton's act of mathematical graffiti, which changed algebra forever.
A hypercomplex number that extends the complex number system into four dimensions. William Rowan Hamilton famously carved their fundamental formula into Dublin's Brougham Bridge on October 16, 1843.
Which modern technology relies heavily on Quaternions to render smooth, glitch-free 3D movements?
What is the name of the mechanical and digital glitch where a rotating system loses a degree of freedom?
007skaty Without up or down in space, onboard computers constantly calculate orientation to keep the International Space Station and satellites pointed correctly.
Which famous 1969 space mission used Quaternions in its onboard guidance computer?