I thought of adding an extra axis..........perpendicular to the other two.....into the 3rd d..............higher dimensions................the next dimension being perpendicular to the others........so I put the imaginary axis above the 2 d paper................i being one unit above paper...............2i, being two units above, etc..........

The book Beyond the 3rd d............stated each new dimension is perpendicular to the others........

Four-Dimensional Geometry -- from Wolfram MathWorld

mathworld.wolfram.com › ... › Interactive Entries › Interactive Demonstrations

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Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) ...

Four-dimensional space - Wikipedia

https://en.wikipedia.org/wiki/Four-dimensional_space

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A four-dimensional space or 4D space is the simplest possible generalization of the ... The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise ... The study of Minkowski space required new mathematics quite different from that of four-dimensional Euclidean ...

‎Four-dimensionalism · ‎Fourth dimension in art · ‎List of four-dimensional games

Fourth Dimension - Math Forum - Ask Dr. Math

mathforum.org/library/drmath/view/54683.html

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May 13, 1997 - 3 posts

Fourth Dimension. ... Will you please help me try to understand what the fourth dimension is? ... In your paper you might discuss what types of functions could describe how the plane travels through this four-dimensional space.

4th dimension in math - part 1 - YouTube

▶ 6:07

https://www.youtube.com/watch?v=Qc2ymRAHvn0

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Mar 6, 2010 - Uploaded by Parth Patel

This video is introduction to the 4th dimension in math. Not the philosophical time, but real 4th dimension.

The 4th dimension can be explained by math but does that mean it ...

https://www.quora.com/The-4th-dimension-can-be-explained-by-math-but-does-that-...

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Using the term "4th dimension" is actually vague when we are talking about mathematics and physics. In math, the would be describing a 4th dimension that is exactly the same as the other three before it: spacial dimensions.

Exotic spheres, or why 4-dimensional space is a crazy ... - Plus Maths

https://plus.maths.org/content/richard-elwes

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Jan 12, 2011 - Like geometry, topology is a branch of mathematics which studies shapes. .... Perhaps after all, the fourth dimension is the right mathematical setting for the .... Can't we just look at the 4th dimension from a 5th dimensional ...