Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.

On this website, my goal is to give you an intuitive understanding of a 4th spatial dimension. To achieve this, we'll first brush up on simple 2D and 3D space, then using that knowledge we'll observe the most fundamental 4D shapes. To begin, …

Interactive Models of 4D Objects The following images link to interactive models of some of the four-dimensional objects we've studied. To use the interactive versions, your browser must support WebGL, and you must have JavaScript enabled in your browser.

2023年7月23日 · It's very hard to properly visualize or even picture 4D technology and objects, and perhaps the best method is to compare 2D images and 3D models. We can directly see the key differences between a 2D square and 3D cube, and the transition to 4D would be a similarly significant paradigm shift.

2017年4月26日 · Plotting four dimensions in the xyzw coordinate system. One commonly explored 4D object we can attempt to visualize is known as a hypercube. A hypercube is analogous to a cube in 3 dimensions, just as a cube is to a …

2023年9月20日 · Four-Dimensional Space (4D): In physics, time is often considered the fourth dimension, essential in understanding space-time in Einstein's theory of general relativity. Euclidean n-Dimensional Space (nD) : It's a way of thinking about space that goes beyond our usual three dimensions.

2017年5月18日 · If you want an example of a 3D object living in a 4D space, you can take the unit hypersphere given by the equation $x^2+y^2+z^2+t^2=1$. Try to find out how it projects on a few hyperplanes!

There are also plenty of other 4D object representations you can find or create yourself. Maybe instead of perspective projection you use stereographic projection. Perhaps you unfold the object into a 3D net.

2023年7月6日 · This article will explain how to render 4D objects in Unity, using three separate technique: orthographic projection, perspective projection and cross-section. You can find all the articles in this series here: Part 1: Understanding the Fourth Dimension; Part 2: Extending Unity from 3D to 4D; Part 3: Rendering 4D Objects; Part 4: Creating 4D ...

2024年11月5日 · These pages contain information about various 4D objects and many images of their projections into 3D. The regular polychora: the 4D equivalents of the Platonic solids. The uniform polychora: the 4D equivalents of the uniform polyhedra, including the Archimedean solids and the prisms and antiprisms.