Relative change in the context of Factor of safety

Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.

Geodynamical phenomena, including crustal motion, tides, and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems.

Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for ${\displaystyle A}$ grows at a faster rate than ${\displaystyle B}$ (i.e. ${\displaystyle A}$ grows proportionally more than ${\displaystyle B}$), ${\displaystyle A}$ should not lose a seat to ${\displaystyle B}$. More formally, if the ratio of votes or populations ${\displaystyle A/B}$ increases, then ${\displaystyle A}$ should not lose a seat while ${\displaystyle B}$ gains a seat. An apportionment method violating this rule may encounter population paradoxes.

A particularly severe variant, where voting for a party causes it to lose seats, is called a no-show paradox. The largest remainders method exhibits both population and no-show paradoxes.

In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula$${\displaystyle {\frac {f'}{f}}}$$where f′ is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely f′ scaled by the current value of f.

When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln f(x), or the natural logarithm of f. This follows directly from the chain rule:$${\displaystyle {\frac {d}{dx}}\ln f(x)={\frac {1}{f(x)}}{\frac {df(x)}{dx}}}$$

Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D space. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. Geodetic job titles include geodesist and geodetic surveyor.

Through highly accurate observations, geodesy provides the scientific basis for mapping, navigation, and positioning, and supports applications such as infrastructure development (including construction), natural resource management, mineral exploration, and geophysics. Its measurements underpin modern geospatial reference frames used in transportation, satellite systems, global trade, and timekeeping.