![]() Medicine, Oncology, Dentistry, Physiology, Epidemiology, Infectious Disease, Pharmacy, Human Body Psychology, Cognitive Psychology, Developmental Psychology, Abnormal, Social Psychology Social Science, Political Science, Economics, Archaeology, Anthropology, Linguisticsīiology, Evolution, Morphology, Ecology, Synthetic Biology, Microbiology, Cellular Biology, Molecular Biology, Paleontology Mechanical Engineering, Electrical Engineering, Structural Engineering, Computer Engineering, Aerospace EngineeringĬhemistry, Organic Chemistry, Polymers, Biochemistry Mathematics, Statistics, Number Theory, Calculus, AlgebraĪstronomy, Astrophysics, Cosmology, Planetary FormationĬomputing, Artificial Intelligence, Machine Learning, ComputabilityĮarth Science, Atmospheric Science, Oceanography, Geology Theoretical Physics, Experimental Physics, High-energy Physics, Solid-State Physics, Fluid Dynamics, Relativity, Quantum Physics, Plasma Physics /r/AskScienceDiscussion: For open-ended and hypothetical questions.FAQ: In-depth answers to many popular questions.Weekly Features: Archives of AskAnything Wednesday, FAQ Fridays, and more!.Be civil: Remember the human and follow Reddiquette.Report comments that do not meet our guidelines, including medical advice.Downvote anecdotes, speculation, and jokes.Upvote on-topic answers supported by reputable sources and scientific research.Answer questions with accurate, in-depth explanations, including peer-reviewed sources where possible. ![]() This is always the case for the boundary of a shape in any dimension – consider the circle, C = 2(pi)r is the derivative of A = (pi)r^2, or the sphere volume & surface area formulae.Please read our guidelines and FAQ before posting You may notice the (n-1)-dimensional surface-volume is the derivative of the n-dimensional volume. When s = 2n (side length = 2 x number of dimensions) these formulae will yield equal results. (n-1) dimensional surface-volume = (2n) x s^(n-1) Generally, an n-dimensional cube with side lengths s has: (I can’t prove this, but a little internet research reveals it!) ![]() The number of (n-1)-dimensional boundary elements of an n-dimensional cube is 2n.Ī 4d hypercube has 8 x 3d cubes surrounding The 3-dimensional surface-volume (akin to surface-area) would indeed be 8 x 8^3, so this would be an equable 4d shape. The 4-dimensional volume of this would be 8^4. I believe the shape you are referring to is a hypercube or tesseract. Can anyone help? Oh, and if you could do it in such a way that a 12 year could understand that’d be great. What is 4D space called? It’s fair to say that my 4D shape work has been somewhat lacking in the past and I feel that I’m now at a stage in my life where I’m happy to delve into 4D. I was able to describe that the 4D shape in question would be bounded (somehow) by 8 cubes of size 8x8x8, which I hope is actually true. What I’d like help with is how to determine if that’s true. Now, I have a couple of students who noticed that in 2D, a 4×4 shape is equable and in 3D, a 6圆圆 shape is equable and so, they suggested that in 4D, an 8x8x8x8 shape should be equable with volume = to hypervolume? It’s really nice to get to the point where students are actually asking if they can use algebra to solve something. This is the perfect cue for “You’re right, there is a quicker way…” and demonstrating an algebraic approach. Usually, someone eventual points out that just trying rectangles isn’t very efficient or, more bluntly, calls it tedious. In year 8 (ages 12 and 13), we have a project called Equable Shapes which starts off with trying to find a rectangle where the area and perimeter have the same value (ignoring units). Students often stumble across some through trying various shapes and are more successful if they are systematic in their approach. ![]()
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