WAIT
- Locked due to inactivity on Aug 4, '16 4:23pm
Thread Topic: WAIT
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Tritanope NewbieIf length*width= area^2 in a square, length*width*height= volume^3 in a cube, then length*width*height*4th dimension= 4th dimensional volume^4 in a 4-dimensional cube?
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Tritanope NewbieTesseract
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Tritanope NewbieIn response to my post "Wait...so, if length*width= area^2 in a square, length*width*height= volume^3 in a cube, then length*width*height*4th dimension= 4th dimensional volume^4 in a 4-dimensional cube?" I'll try to explain more in depth if I can.
A square. Length multiplied by width equals area. So if I had a 3 length and a 3 width, area would be 9 units squared (^2, or second power. Facebook won't let me use exponents...it makes my eyes hurt, too). It is 9 units squared because to get to 9, you have to take 3 to the second power, and you must use the second power as there are 2 dimensions involved: length, and width.
A cube. This is EXACTLY like a square, but now there's a third dimension. This third dimension is known as height. Length times width times height equals volume. So now you have a 3 length, a 3 width, and a 3 height. 3x3x3=27. 3x3x3 is also known as 3^3 or 3 to the third power [third power= cubed]. What happened? Same as in the square, since we are now working in 3 dimensions we must use the third power. Length, width, and height. Space goes in all of those directions.
But...tesseract? Hypercube? 4-cube? What is this sorcery? Just EXACTLY like a square or cube, but with 4 dimensions of space! Now we have space going in 4 dimensions rather than 3! (Hard for me to visualize, but I can represent it with geometry and numbers.) The 4th dimension is not named, so I'll call it 4Dim. Length times width times height times 4Dim equals 4Volume! So 3 length, 3 width, 3 height and 3 4Dim is 3x3x3x3...3^4 or 3 to the fourth power (3...fourthed?)!
Simply taking the length of one side to the 4th power only gives you the 4 dimensional volume if all sides are equal in length. I used the same measurement for everything. If you had...5 length, 6 width, 7 height, and 8 4-dimension, you would need 5x6x7x8 to equal 4 dimensions, even though you would still write the result as result^4 like how when finding area you write the result as result^2.
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