For smooth level surfaces $f=0$, $g=0$ meeting at a point where both gradients are nonzero, their acute angle is the angle between two planes tangent to the surfaces there. Each gradient is a normal vector to its tangent plane, proving the displayed formula. Vanishing gradients require further analysis because the level-set equation then need not specify a unique tangent plane.

A plant genus used to investigate floral development.^[ref]

A legume genus whose radial flowers provide an example in which an apparent reversal of floral symmetry can reflect expanded dorsal organ identity.^[ref]

A lossless low-energy charged-condensate action has a positive compressibility coefficient ${\chi }_p$, effective pair density ${\rho }_0$, mass $m_{\ast }$ and signed charge $q$. Coupling its phase to the electromagnetic potentials through the displayed combinations preserves gauge symmetry. Adding the Maxwell action and eliminating the longitudinal electric potential gives ${\omega }^2=q^2{\rho }_0/({ϵ}_0{m}_{\ast })+[{\rho }_0/(m_{\ast }{\chi }_p)]k^2$ in a simple homogeneous bulk model. Removing the electromagnetic coupling leaves neutral sound. Static Ginzburg-Landau theory of superconductivity alone cannot determine these frequencies or their damping. ^[ref]

A salamander used experimentally to investigate limb regeneration and lineage contributions to the regenerative outgrowth.

The frog total group, including Anura and extinct stem relatives such as Triadobatrachus massinoti.

A salamander is an amphibian with a typically elongated body and a tail retained in the adult. Development varies from metamorphosis to retention of larval features. This variation makes salamanders useful for comparing biological development and life-history evolution.

An amino acid with a side chain containing an imidazole ring. Its metal-coordination properties support purification through a histidine tag.

asparagine is an amino acid with a side-chain amide. Its side-chain nitrogen is the usual attachment site in canonical N-linked protein glycosylation.