Simple really.
The longdome etc needs some rather heavy mathematics, which i don't have.
The thing is that [(w,x),(y,z)] is a specific formula for content of a general bi-elliptical prism, and ([w,x],[y,z]) is a formula for a bi-square-spheroid.
I use feet and inches in atomic constants as well. it's no big deal.
Even moments of inertia will change depending on the mode of operation
The longdome etc needs some rather heavy mathematics, which i don't have.
I was thinking we might get the tensile strength od 4d-carbon from the physics and chemistry of 4d-carbon. You would use QM but I might require a periodic table. I don't know. Any ideas?
I don't know how much maths is needed to handle a longdome, or a spherotegmate figure. Sometimes they are dirt-easy, sometimes, they are hard. But in these, the volume can be written as the tegmate product of surface and radius, and so finding one finds the other.
Dome is not an intersection of two cylinders, but its volume can be found pretty easily:
First, we review its properties: It has to cast two circular shadows (when we remove the end-nodes) and one square shadow (removing the middle-node). Passing it through the plane will result in two possibilities: either a square that will start from a point, grow, then shrink...
...or we start with a line. This will grow into circle (originally I thought it was through ellipse, but in fact the intermediate shapes are circles with their top and bottom cut). Then it shrinks back into line.
If we put all relevant edge lengths / diameters as 2, we get
Surface are is then equal to 16 (volume times dimension). I'm not sure what are the exact condition for this simple surface formula to hold, but according to Wendy it should work for all rotatopes as long as they have all cross-dimensions 2.
The density of 4d-man is (100 kg)/(2 m)/(.2 m)/.1m)/(.1 m)=.25*10^5 kg/m^4=25 g/cm^4. This gives a measure of the density of Carbon.
Thus, 9.8 m/sec^2=G mp /r^3 = G(10^5 kg/m^4 *r^4)/r^3=G(10^5 kg/m^4)r, thus giving an inverse realtion between r & G :rp = 4*10^-4/G/(kg/m^4), based merely on an earthlike man and some constant G.
moonlord wrote:They appear in alkaline's introduction. So that's no problem.
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