Gauss Law .. .. and Nature's beau stripes !!

 

Remember a Danush / Sivakarthikeyan movie (where they attend a tuition centre) – the master would ask about ‘Gauss law’ – and that provoked to read something. 

Geometry (from Ancient Greek (geōmetría) 'land measurement')   is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. 

Geometry is all about lines -  lines in geometry can be classified into several types, primarily categorized as straight or curved. Straight lines can be further defined as horizontal, vertical, parallel, intersecting, or perpendicular.

 

Here is God’s creation with lines … .. an equine called Zebra.  Zebras  are African equines with distinctive black-and-white striped coats. There are three living species: Grévy's zebra (Equus grevyi), the plains zebra (E. quagga), and the mountain zebra (E. zebra). Zebras share the genus Equus with horses and asses, the three groups being the only living members of the family Equidae. Zebra stripes come in different patterns, unique to each individual. Several theories have been proposed for the function of these patterns, with most evidence supporting them as a deterrent for biting flies.   

Johann Carl Friedrich Gauss [1777 –1855] was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces Disquisitiones Arithmeticae and Theoria motus corporum coelestium. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science and mathematics, more than 100 mathematical and scientific concepts are named after him. 

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and their rates on a surface, without reference to the particular manner in which the surface is embedded in the ambient 3-dimensional Euclidean space. In other words, the Gaussian curvature of a surface does not change if one bends the surface without stretching it. Thus the Gaussian curvature is an intrinsic invariant of a surface.

 
Interesting !!  ~  here is a Zebra pictured at Bannerghatta zoological park.
 
Regards – S Sampathkumar
2.6.2025