A **spherical conic** is a curve that can be defined on the surface of a sphere, analogous to conic sections in a plane, such as ellipses, parabolas, and hyperbolas. While traditional conic sections are produced by the intersection of a plane with a double cone, spherical conics arise from the intersection of a sphere with a plane in three-dimensional space.

In topology, a surface is a two-dimensional topological space that can be defined informally as a "shape" that locally resembles the Euclidean plane. More specifically, a surface is a manifold that is two-dimensional, meaning that every point on the surface has a neighborhood that is homeomorphic (topologically equivalent) to an open subset of \(\mathbb{R}^2\). ### Key Features of Surfaces: 1. **Local vs.

Astranis is a company focused on developing small, affordable satellites that provide internet connectivity, particularly for underserved regions. Founded in 2015 and based in San Francisco, Astranis aims to bridge the digital divide by leveraging technology to offer reliable internet access in areas where traditional infrastructure may be lacking or too costly to deploy. Their satellites are designed to be smaller and more cost-effective compared to traditional communication satellites, making it easier and more economical to deploy broadband services.

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. It describes the shape of the molecule formed by the positions of the bonded atoms and the angles between them. Understanding molecular geometry is crucial in chemistry because it influences properties such as polarity, reactivity, phase of matter, color, magnetism, biological activity, and many other characteristics of molecules.

Thales of Miletus was an ancient Greek philosopher, mathematician, and astronomer, born around 624 BCE in Miletus, a city in Ionia (modern-day Turkey). He is often considered one of the founding figures of Western philosophy and is one of the earliest known pre-Socratic philosophers. Thales is particularly credited with shifting the focus of Greek thought from mythological explanations of the world to rational ones based on observation and inquiry.

Gerd Faltings is a German mathematician known for his significant contributions to number theory and arithmetic geometry. He was born on July 28, 1954, and is best known for his work on the theory of Diophantine equations, particularly for proving the Mordell conjecture in the 1980s.

Wei Zhang is a prominent mathematician known for his contributions to number theory, specifically in the areas of automorphic forms and representation theory. He has made significant advances in understanding the connections between number theory and other areas of mathematics, including algebraic geometry and harmonic analysis. Zhang's work includes investigations into the Langlands program, which seeks to relate number theory and representation theory through a series of conjectures and theories.

August Ferdinand Möbius was a German mathematician and astronomer born on November 17, 1790, and he passed away on September 26, 1868. He is best known for his contributions to topology, particularly for the introduction of the Möbius strip, a surface with only one side and one boundary.

The Huygens–Fresnel principle is a fundamental concept in the field of wave optics that describes how waves propagate and interfere. Named after Dutch physicist Christiaan Huygens and later expanded by the French physicist Augustin-Jean Fresnel, the principle provides a way to analyze the propagation of wavefronts, such as light waves.

Friedrich Otto Rudolf Sturm, also known simply as Fritz Sturm, is a renowned figure in the field of mathematics and is known for his contributions to various areas including differential equations, control theory, and numerical analysis.

Howard Eves was a notable American mathematician, known for his contributions to geometry, particularly in the realms of mathematics education and mathematical history. Born in 1888 and passing away in 1975, Eves served as a professor and authored several influential textbooks and papers. He is particularly recognized for his work on the history of mathematics and for promoting the understanding of mathematical concepts through engaging teaching methods. His books on geometry and mathematical history remain significant resources in the field.

James B. Carrell was a notable American mathematician known for his contributions to the field of mathematics, particularly in algebra and topology. He is recognized for various mathematical concepts and theorems, although detailed information about his life and specific works may not be widely documented.

Johannes Hjelmslev (1899-1965) was a Danish linguist and a key figure in the development of structural linguistics in the 20th century. He is best known for his work in the field of semiotics, the study of signs and their meanings, as well as for his contributions to the theory of language structure.

Leroy Milton Kelly, often referred to simply as "Leroy Kelly," is a former American football player known for his time as a running back in the National Football League (NFL). He played for the Cleveland Browns from 1964 to 1973. Kelly was a versatile and talented player, known for his speed and agility on the field. During his career, Kelly was a key player for the Browns and was inducted into the Pro Football Hall of Fame in 1994.

Lorenzo Mascheroni (1750–1800) was an Italian mathematician known for his contributions to geometry and for his work on the relationship between geometry and the mathematics of numbers. He is particularly renowned for Mascheroni's theorem, which asserts that any Euclidean construction that can be accomplished using a compass and straightedge can also be performed using only a compass. This result has implications for the foundations of geometry and the nature of geometric constructions.

As of my last knowledge update in October 2023, "Nelli Neumann" is not a widely recognized term or name in popular culture, science, or notable events. It could refer to a person, a business, or something else that may not be well-known or indexed in major databases.

Oskar Bolza (1857–1942) was a notable German mathematician, particularly recognized for his contributions to the fields of analysis and differential equations. He played a significant role in developing mathematical theories during the late 19th and early 20th centuries. Bolza is known for the Bolza problem in calculus of variations, which deals with finding the extremal functions for a given integral that also satisfies certain constraints.

Richard M. Pollack is a prominent American scientist known for his research in the fields of biology and biophysics. He is particularly recognized for his work on the mechanisms of molecular motors and their role in cellular processes. His research often intersects with topics such as energy conversion, protein structure, and the physical principles underlying biological functions. Pollack has published numerous scientific papers and has contributed to the understanding of how molecular machines operate at the cellular level.

Robert Williams is a mathematical geometer known for his work in the field of differential geometry and topology. His research often intersects with various areas of mathematics, including algebraic geometry and the study of manifolds. Williams has made notable contributions to the understanding of geometric structures and their properties. One of his significant contributions includes work on dynamical systems and their geometric aspects.