This is just something I thought up but I'm near certain it is correct.
Area and volume
1 Dimension = 10cm
2 Dimensions = 10cm * 10cm=100cm squared (assuming each side of the rectangle has the the same amount)
3 Dimensions = 10cm * 10cm * 10cm=1000cm cubed (assuming each side of the cube has the the same amount)
4 Dimensions???? = 10cm * 10cm * 10cm * 10cm=10000cm to the fourth (assuming each side of the 4-dimesional cube has the the same amount)
I think you could do this an unlimited amout of times.
This is some stuff on the subject(in relation to string theory which is still theory): If I'm not mistaken the equation looks just like mine at the end of the second link (which shows a cube in 4 dimensions)
http://www.pbs.org/wgbh/nova/elegant/dimensions.html
http://www.pbs.org/wgbh/nova/elegant/math-flash.html
Hope this helps.
Note: This is for spatial dimensions the calcuation for temporal(time) dimensions are different if I remember correctly.
Area and volume
1 Dimension = 10cm
2 Dimensions = 10cm * 10cm=100cm squared (assuming each side of the rectangle has the the same amount)
3 Dimensions = 10cm * 10cm * 10cm=1000cm cubed (assuming each side of the cube has the the same amount)
4 Dimensions???? = 10cm * 10cm * 10cm * 10cm=10000cm to the fourth (assuming each side of the 4-dimesional cube has the the same amount)
I think you could do this an unlimited amout of times.
This is some stuff on the subject(in relation to string theory which is still theory): If I'm not mistaken the equation looks just like mine at the end of the second link (which shows a cube in 4 dimensions)
http://www.pbs.org/wgbh/nova/elegant/dimensions.html
http://www.pbs.org/wgbh/nova/elegant/math-flash.html
Hope this helps.
Note: This is for spatial dimensions the calcuation for temporal(time) dimensions are different if I remember correctly.