| Developer: | Ferenc Gerlits (1) | ||
| Price: | Free | ||
| Rankings: | 0 | ||
| Reviews: | 0 Write a Review | ||
| Lists: | 0 + 0 | ||
| Points: | 0 + 87 (4.1) ¡ | ||
| Google Play | |||
Description
To show himself to the Square, the Cube first moves up and down through Flatland face-first. What the Square sees is another square (the horizontal intersection of the Cube with Flatland) suddenly appearing out of nowhere, then staying put for a while, and then disappearing again. Next, the Cube rotates itself and moves up and down edge-first. Now the Square sees a line appearing out of nowhere, which turns into a long narrow rectangle, which gets wider and wider for a while, then it gets narrower and narrower again, until it turns back into a line and then it disappears. Finally, the Cube rotates itself once more, and moves up and down vertex-first. Now the Square sees a point appearing out of nowhere, which turns into a small triangle, which gets larger and larger for a while, then its vertices get cut off and it turns into a hexagon. When the Cube is exactly half way through, the Square can see the Cube's horizontal intersection with Flatland as a regular hexagon. As the Cube moves further, the hexagon turns back into a triangle, which then gets smaller and smaller, and finally the triangle turns into a point and disappears.
This app does the same thing one dimension higher. Instead of a Cube visiting people who live in a two-dimensional plane, it shows a Hypercube (four-dimensional cube) visiting people, like you and me, who live in a three-dimensional space.
When the app starts, the Hypercube is sitting face-first exactly half way through our three-dimensional space. We can see the "horizontal" intersection of the Hypercube with our space, which, as you have probably guessed, is a three-dimensional cube.
You can move the cube around in our space by dragging it with your fingers. It has six colored faces, which are the intersections of our space with six of the eight colored faces of the Hypercube. Each face of the Hypercube has a different color.
You can move the Hypercube "up" and "down" in the direction of the fourth dimension using the red slider. This direction is perpendicular to all our three coordinate axes x, y and z, and is just as difficult for us to imagine as our up and down are to the people of Flatland.
To make more interesting shapes, you can rotate the Hypercube using the three blue sliders. These sliders rotate the Hypercube around the pairs of axes xy, xz and yz, respectively. It is not hard to see that as you can rotate a cube in three-dimensional space around any one axis, you can rotate a hypercube in four-dimensional space around any pair of axes.
Try to set the blue sliders to make the Hypercube move through our space two-dimensional-face-first, edge-first, and vertex-first! This takes some thinking, but it's not difficult. Then move the Hypercube "up" and "down" using the red slider, and see how the intersection of the Hypercube with our three-dimensional space changes. What is the intersection exactly half way through in each of these three directions?
What is the most interesting shape you can make? What is the largest possible number of faces? What is the largest possible number of vertices?
Hypercube Viewer is free software. You can browse and download the source code at https://github.com/fgerlits/hypercube
* in the book, it's a Sphere, but spheres are boring
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Developer
- Ferenc Gerlits
- Platforms: Android Apps (1)
- Lists: 0 + 0
- Points: 0 + 87 ¡
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Additional Information
- Version: 1.5
- ID: ferenc_gerlits.hypercube_viewer
- Category:
Android Apps›Education - OS:
Android 5.0 - Size:
21 Mb - Content Rating:
Everyone - Google Play Rating:
4.1(87) - Updated:
- Release Date:
«Hypercube Viewer» is a Education app for Android, developed by «Ferenc Gerlits». It was first released on and last updated on . This app is currently free to download. This app has not yet received any ratings or reviews on AppAgg. On Google Play, the current store rating is 4.1 based on 87 votes. AppAgg continuously tracks the price history, ratings, and user feedback for «Hypercube Viewer». Subscribe to this app or follow its RSS feed to get notified about future discounts or updates.
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