Ribbons, Rings and Yoda

From "Torus Starts Here",

${ L_{ or } }^{ 2 }=( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }$

We have the surface area of the ribbon extended by the helical torus,

$A_r=\cfrac{1}{2}.2\pi r.r=\cfrac{1}{2}L_{or}.r_p$

$A_r=\cfrac{1}{2}r_p\left\{( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\right\}^{1/2}$

$A_r=\pi r_p\left\{(  r_{or})^2 +( n r_{ p } ) ^{ 2 }\right\}^{1/2}$

If we imagine stacking such ribbons into a torus, we have the volume of a torus as,

$V_{tor}=\lambda A_r=\lambda\cfrac{1}{2} r_p\left\{( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\right\}^{1/2}$

$V_{tor}=\cfrac{1}{2}\cfrac{L_{cir}}{n} r_p\left\{( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\right\}^{1/2}$

$V_{tor}=\cfrac{\pi }{n}r_{or} r_p\left\{( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\right\}^{1/2}$

$V_{tor}=\cfrac{2\pi^2 }{n}r_{or} r_p\left\{(  r_{or})^2 +( n r_{ p } ) ^{ 2 }\right\}^{1/2}$

Similarly, the surface area of a torus is given by,

$A_{tor}=\lambda L_{or}=\cfrac{2\pi r_{or}}{n}\left\{( 2\pi r_{or})^2 +( n2\pi r_{ p } ) ^{ 2 }\right\}^{1/2}$

$A_{tor}=\cfrac { \left( 2\pi  \right) ^{ 2 }r_{ or } }{ n } \left\{ (r_{ or })^{ 2 }+(nr_{ p })^{ 2 } \right\} ^{ 1/2 }$

Which must be reconsidered deeply.  Mediate on it I will.