Equation 7 · Einstein's Random Walk and the Mathematics of Genetic Drift
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol D
D is part of the quantity the equation computes from the expression on the right.
Symbol N
N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol pi
pi occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol k
k occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →Denominator: 6pi k P
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
with the diffusion constant D fixed by measurable quantities. Einstein derived it explicitly, from the balance between the drag on a sphere of radius P in a fluid of viscosity k and the osmotic pressure driving diffusion, as . where R is the gas constant, T the absolute temperature, and N Avogadro’s number [ 1 ] . That last dependency was the trap door: if D could be read off a microscope by timing how far a particle wandered, and every other term in the equation was already known independently, then watching one particle jiggle became a way to count atoms.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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