An image search for “hypercube” will give results which are mostly fixed-perspective views of something like this structure, but in a static way: So, then, how do we illustrate the hypercube? Well, it turns out that this question has a pretty complicated answer. What does this graphic suggest about the 4-cube? This gives an infinite sequence of n-cubes, or n-dimensional “cubes”, where n = 0, 1, 2, 3, 4, 5, … (That’s right there are “cubes” in much higher dimension than 4! But let’s not get ahead of ourselves.) Here’s a graphic illustrating the n-cubes we’re familiar with. In fact, even a square is just a 2-dimensional extension of a line segment, which is itself a 1-dimensional extension of a point. What’s a hypercube?Ī hypercube (or tesseract) is the 4-dimensional “extension” of a cube in the same way that a cube is the 3-dimensional extension of a square. But my favorite topic to teach in this course was that of dimension…specifically, dimension 4. I usually taught a grab-bag of super fun topics like the (cultural) history of numbers and computation, symmetry and tessellations, chaos and fractals, and the notion of infinity. It was designed specifically for non-science students to get their required math credit, so there was a lot of flexibility with respect to the course’s content. At Saint Mary’s College, I frequently taught a class called Art & Practice of Math. The other part was (unsurprisingly?) mathematics. If you’ve ever been to the Exploratorium in San Francisco (one of the most magical places in the world, if you’re a lover of science and gadgets, like me), you’ve likely seen several examples of zoetropes, including the one featured in the video above! In fact, seeing that very 3D zoetrope at the Exploratorium was a big part of what inspired me to dream this project up in the first place. If the synchronization isn’t exact, these 16 positions will seem to rotate around the center, as a group. So what the viewer sees is a quick succession of the still arrangements, which gives the illusion of motion at each of the 16 positions along the outside of the base. This means that for each revolution of the base, the strobe should flash 16 times. Examination of the video above shows that there are 16 penguin arrangements along the circumference of the base. This 3-dimensional zoetrope uses a very different sort of device to focus its viewer’s attention on a single point (in time): illumination by a strobe light, whose flash frequency is synchronized with the frequency of the rotating base, also taking into consideration the number of still objects contained in the zoetrope. This amazing zoetrope is the work of Gary and Danny Aden, and now lives at the Exploratorium in San Francisco. In this type of zoetrope, a carefully-timed strobe light helps the viewer focus their attention on individual frames. Isolating the individual frames of the motion is key to focusing the viewer’s attention on exactly one point (thereby avoiding a blur).Īn example of a 3-dimensional zoetrope, which uses still 3D objects to animate motion in space. When the circular base is rotated at a constant speed, a viewer which is focused on a single point along the circumference of this contraption will perceive motion.
ROTATING HYPERCUBE FREE
cylinder or flat disc) that is free to rotate about its central axis.
ROTATING HYPERCUBE FULL
The still objects, which represent instantaneous and sequential “snapshots” (taken at equal intervals), through one full period (cycle) of the motion, are placed uniformly (equally-spaced) along the circumference of some object with circular symmetry (e.g. What’s a zoetrope?Ī zoetrope is a mechanical device which animates still images or objects to create an illusion of periodic (repeating/looping) motion. But if you’re not, here’s an explanation. Now, if you’re a mathy person, that description (mostly) makes sense. In case you’re wondering what I’ve been up to, it’s this: I’m building a zoetrope that animates the “shadow” of a hypercube which is performing a double rotation in 4-dimensional space.
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