8/9/2023 0 Comments Desmos 4d sphereJust as the 2D shadow of a 3D object can be observed, we can study the 3D shadow of a 4D object to visualize rotations in 4D space. 3 Answers Sorted by: 9 The simple answer is that your cousin could be correct. You can see the analogy of the 3D cube held up to the light source and projected down into 2D, and the shadow of its 4D equivalent. ![]() Stereographic projections allow us to observe the shadow of a higher dimensional object by holding it up to a light source in its dimension. The Stereographic Projection Visualization is a project dedicated to demonstrating the concept of stereographic projections visually and intuitively. For example, in 3D, a rotation about the XY plane correlates to a rotation about the Z-axis, but with the inclusion of another spatial dimension, there is no axis of rotation, only a hyperplane. In 4D, however, this is impossible, as rotations are associated with hyperplanes. Rotations in 4D space are difficult to visualize, especially due to the fact that rotations are often associated with an axis. ![]() s/o to Kyle Pearce for the videos, another s/o to Jay Chow for the cone/sphere graph. The 4D Coordinate Axes are the result of some playful math, and some curiosity to see how rotations affect the 6 different hyperplanes in 4D space. After studying the volume of cylinders and cones, we now will investigate the volume of a sphere. Two more graphs to add to my four-dimensional graph series. Graph #2 - Stereographic Projection Visualization Rather than just draw on the whiteboard all day in front of a bunch of students, I turned to Desmos, and thus the AP Calculus BC and Multivariable Calculus pages were born on my website (although they could use some cleaning up! haha). My job was to provide any resources I could find or create that would help the learning process of the students in the classroom. This also stemmed from the fact that I did very well in my HS Calculus class, to the point where my teacher had me working as a teacher assistant the next year. This way, I can help someone else that may be struggling where I am as well. I'm more of a visual learner, so whenever I come across a new topic in math that I have a hard time understanding, I construct a Desmos graph based on that topic, and as I gain a better understanding, I also end up with a product that portrays an intuitive visual understanding of the topic. I spend most, if not all, of my free time learning new mathematics and creating content. I've given up a life of video games in exchange for Desmos and studying math. NLERP is equivalent (in this case) and may be faster, but it would have taken a few more equations to implement in Desmos.Not exactly, in fact I still have yet to start college. The arcs between the points are generated using SLERP (, derivation at ). The only points displayed are those on the "camera side" of the sphere, which is done using dot product Mathematically, this is done using geometric algebra in a manner isomorphic to using quaternions. These are randomly generated by choosing an axis (in the same we we chose a random point) and rotating about it with an angle equal to T (from 0 to τ). The points move around in circles on the sphere. ![]() This (x,y,z) distribution is spherically symmetric, so we can divide by its distance from the origin to normalize it to lie on the unit sphere To randomly generate points on the sphere, we first take (x,y,z) sampled from three independent normal distributions. To see the underlying sphere and great circles, unhide lines 76 and 77 respectively. This set was first defined and drawn by Robert W. Essentially, this is just a bunch of points moving in circles (not necessarily great circles) around a unit sphere, and nearby points are connected using arcs. Curved Surface Area of Cones (Combined Version) Octahedron and Boat. The Mandelbrot set (/ m æ n d l b r o t,-b r t /) is the set of complex numbers for which the function () + does not diverge to infinity when iterated from, i.e., for which the sequence (), (()), etc., remains bounded in absolute value. Inspired by made by fadaaszhi, which was in turn inspired by a random GIF in the Discord.
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