## Different worlds in Virtual Reality

The great potential of Virtual Reality technology can be fully unleashed when we create realistic simulation of our world. But there is an even more interesting use of VR, that can not be matched by anything else: simulation of mathematical spaces, such as hyperbolic spaces, four dimensional worlds, or Einstein’s space-time.

So, put your VR headset on and let’s take a closer look to something you’ve never seen before!

**HYBERBOLIC VR**

If you are studying, or if you have just heard something about non-Euclidean geometry and you want to *see* it, you can’t miss Hyperbolic VR, an alternative world created by Hart, Hawksely, Matsumoto and Segerman. Visiting h3.hypernom.com you will be able to move through this alternative world, where the basic rules of geometry we know do not apply: you can experience, for instance, how parallel lines can intersect or veer apart.

By entering this world, you can understand non-Euclidean geometry easier than analyzing it via abstract mathematical models or formulas… and if you think this is just a weird stuff, with no connection to reality, just remember that Universe itself is a non-Euclidean space!

**Figure 1**: Non-Euclidean virtual reality I: explorations of H^{3}(retrieved on March 26th, 2020, from: https://arxiv.org/pdf/1702.04004.pdf)

**4D Toys**

Are you bored of your conventional 3D toys? Looking for something new? The fourth dimension is here to entertain you! *4D Toys* is an extremely interactive immersion into a 4D world: you must move objects through the fourth dimension by picking them up, then sliding a finger on a touch surface to move back and forth in 4D space. Instructional text appears and reacts to your every grab of objects and swipe through four-dimensional space.

In this strange world, we, as 3D beings, can just see a section of a 4D object: for this reason, 4D toys “change their shapes” as they move, but only because we can not see through the fourth dimension. Still too complicated? Do you feel like living in Flatland and talking to the Sphere? Maybe experiencing the fourth dimension could be easier than trying to imagine it!

**Figure 2: **4D Toys

(Image courtesy mtb design works, inc.)

**Captain Einstein**

Could you imagine a world where the light speed is 20km/h? And, if you can, could you imagine how the world around you would look like, as soon as you approach gradually to the speed of light? Well, Ghent University created *Captain Einstein*, a VR movie that allows the visualization of the effects of Einstein’s Theory of Relativity during a boat trip in the city: rainbows in the sky, due to the infrared radiation, and space-time distortion.

The VR viewing experience gives you the chance to *feel* the Theory of Relativity by seeing its effects on the surroundings. And, after that, if you really want to understand what stands behind the creation of such a movie, you can always take another trip (this time, at your own speed!) on http://captaineinstein.org/.

**Figure 3: **Captain Einstein – Original Boat tour since 1905

(image retrieved from http://captaineinstein.org/)

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