Terrasects and the fourth-dimension

  • Context: Undergrad 
  • Thread starter Thread starter Benito12
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Discussion Overview

The discussion centers around the concept of terrasects, which appears to be a misunderstanding of tesseracts, and how to represent them on paper. Participants explore the challenges of visualizing and drawing higher-dimensional objects, particularly the fourth dimension.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant seeks guidance on creating a terrasect on paper, indicating a desire to understand higher-dimensional geometry.
  • Another participant corrects the term "terrasect" to "tesseract" and provides a link to a visual representation, suggesting a hands-on approach using toothpicks.
  • A different participant questions the clarity of the linked diagram, asserting that it represents a three-dimensional shadow of a tesseract rather than the tesseract itself.
  • One participant explains that while a three-dimensional cube cannot be fully represented on a two-dimensional surface, various projections can be drawn, paralleling this with the representation of a tesseract in three-dimensional space.
  • This same participant elaborates on the nature of projections, noting that viewing a website on a flat screen is itself a projection of a three-dimensional object that represents a four-dimensional object.

Areas of Agreement / Disagreement

Participants express differing views on the terminology and representation of tesseracts, with no consensus reached on the clarity of the visual representations discussed.

Contextual Notes

There is ambiguity regarding the definitions of terrasects and tesseracts, as well as the nature of their projections. The discussion does not resolve the mathematical or conceptual complexities involved in visualizing higher dimensions.

Benito12
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I just learned about terrasects and the 4th-Dimension, I would like to know how you can make a terrasect on paper.(If it's possible)
 
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The text on that page isn't very clear but my understanding is that the diagram is not of a tesseract but of its three dimensional shadow.
 
thanx :)
 
You can't put a three dimensional cube on a 2D piece of paper but you can draw all sorts of projections of a cube on the flat paper. The typical isometric and perspective drawings are just two.

Just the same, you can't put a 4D tesseract into 3D space but you can make all sorts models that are different projections of it into 3D space. The link in post#2 is one such.

In fact, if you get that website on your (flat) computer screen, you are looking at a 2D projection of a 3D object that is itself a 3D projection of a 4D object; if you can get your head around that!
 

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