The Method of Mechanical Theorems convenient to use a little bit of coordinate geometry. If a sphere of radius 1 is placed with its center at "x" = 1, the vertical cross sectional radius formula_2 at any "x" between 0 and 2 is given by the following formula: The mass of this cross section, for purposes of balancing on a lever, is proportional to the area: Archimedes then considered rotating the triangular region between "y" = 0 and "y" = "x" and "x" = "2" on the "x"-"y" plane around the "x"-axis, to form a cone. The cross section of this cone is a circle
Phase-contrast X-ray imaging the length of the wave vector, the length of a wave vector with wavelength of 1 Angstrom and the atomic number. The valid formula under these conditions for the phase shift cross section is: where is the atomic number, the length of the wave vector, and the classical electron radius. This results in the following expressions for the two parts of the complex index of refraction: Inserting typical values of human tissue in the formulas given above shows that is generally three orders of magnitude larger than within the diagnostic X-ray range. This implies that the phase-shift of an X-ray