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Examples include the legs of a centipede, the maxillary and labial palps of an insect, and the spinous processes of successive vertebrae in a vertebrate's backbone. Male and female reproductive organs are homologous if they develop from the same embryonic tissue, as do the ovaries and testicles of mammals , including humans .
In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follow some examples and reasons: The approach of a hawk to its prey in classical pursuit, assuming the prey travels in a straight line. Their sharpest view is at an angle to their direction of flight; this angle is the same as the spiral's pitch. [7]
A classic example of an equivalence group is the vulva precursor cells (VPCs) of nematodes. In Caenorhabditis elegans self-fertilized eggs exit the body through the vulva . This organ develops from a subset of cell of an equivalence group consisting of six VPCs, P3.p-P8.p, which lie ventrally along the anterior-posterior axis. [ 5 ]
In biochemistry, a Ramachandran plot (also known as a Rama plot, a Ramachandran diagram or a [φ,ψ] plot), originally developed in 1963 by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan, [1] is a way to visualize energetically allowed regions for backbone dihedral angles ( also called as torsional angles , phi and psi angles ) ψ ...
The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.
Definition: [7] The midpoint of two elements x and y in a vector space is the vector 1 / 2 (x + y). Theorem [ 7 ] [ 8 ] — Let A : X → Y be a surjective isometry between normed spaces that maps 0 to 0 ( Stefan Banach called such maps rotations ) where note that A is not assumed to be a linear isometry.
Consequently, rectangles exist (a statement equivalent to the parallel postulate) only in Euclidean geometry. A Saccheri quadrilateral is a quadrilateral with two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure. The ...
For example we see the image of the initial regular pentagon under a homothety of negative ratio –k, which is a similarity of ±180° angle and a positive ratio equal to k. Below the title on the right, the second image shows a similarity decomposed into a rotation and a homothety.