Herbert Federer does not seem to be a widely recognized or notable figure in public domains such as literature, science, politics, or pop culture as of my last knowledge update in October 2023. It's possible that he may be a private individual or someone who has gained notoriety after that date.

"Vertical" and "horizontal" are terms used to describe directions or orientations in space. 1. **Vertical**: - Vertical refers to a direction that is oriented up and down. It is perpendicular to the horizontal plane. In a typical Cartesian coordinate system, the vertical direction often aligns with the y-axis. For example, when you think of a tall building or a tree, those objects have a vertical orientation because they rise straight up toward the sky.

Very-long-baseline interferometry (VLBI) is a type of astronomical technique used to achieve high angular resolution imaging of radio sources. It involves the use of multiple radio telescopes located at different geographical locations, often thousands of kilometers apart, which work together to observe the same astronomical object simultaneously.

Arithmetic geometry is a branch of mathematics that merges aspects of algebraic geometry and number theory. It primarily studies the solutions of polynomial equations and their properties over different fields, particularly over number fields and algebraic varieties. Here are some key concepts related to arithmetic geometry: 1. **Algebraic Varieties**: These are geometric objects defined by polynomial equations. They serve as the basic objects of study in algebraic geometry.

As of my last knowledge update in October 2023, Benjamin Kagan does not refer to a widely recognized public figure, concept, or event. It's possible that he could be a private individual or a lesser-known person in various fields, such as academia, business, or arts.

The World Geodetic System (WGS) is a global reference system that provides a framework for geospatial data and mapping. The most widely used version is the WGS 84 (World Geodetic System 1984), which is employed by the Global Positioning System (GPS) and serves as a standard for cartography, geodesy, and navigation.

Boris Delaunay, also spelled as Boris Delaunay in some contexts, is primarily known as a mathematician who contributed significantly to the field of computational geometry. He is best known for the Delaunay triangulation, a method of dividing a set of points into triangles that maximizes the minimum angle of the triangles, avoiding skinny triangles. This triangulation is important in various applications, including computer graphics, geographic information systems (GIS), and finite element analysis.

Boyd Crumrine Patterson was an influential American lawyer and politician who served as a significant political figure in Pennsylvania. He was born on August 4, 1910, and passed away on March 23, 1991. Patterson was best known for his role as a member of the Pennsylvania House of Representatives, where he made contributions to legislative processes and local governance. He played a notable role in advocating for various issues during his tenure, helping to shape public policy in the state.

Børge Jessen is not specifically known as a widely recognized public figure, concept, or term in common knowledge up until October 2023. It is possible that Børge Jessen could refer to an individual, character, or a concept that is less commonly discussed or is specific to a certain region or context.

Hubert Schardin does not appear to be a widely recognized figure in public discourse, historical records, or contemporary news up to October 2023. If you're looking for information about a specific individual or context associated with that name, please provide additional detail, and I'll do my best to assist you. It's possible that Schardin may refer to a less-known individual, a fictional character, or a niche subject not covered in major sources.

"British geometers" typically refers to mathematicians or mathematicians from the UK who have made significant contributions to the field of geometry. Geometry is a branch of mathematics that deals with the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. Historically, several British mathematicians have been prominent in the development of geometry.

Hyperbolic geometers are mathematicians or researchers who specialize in hyperbolic geometry, which is a non-Euclidean geometry characterized by its unique properties and structures. In hyperbolic geometry, the parallel postulate of Euclidean geometry does not hold. Specifically, through a given point not on a line, there are infinitely many lines that do not intersect the given line, in contrast to Euclidean space, where there is exactly one such line.

"Medieval geometers" typically refers to mathematicians and scholars during the Middle Ages who contributed to the field of geometry, building on the foundations established by ancient Greek mathematicians like Euclid, Archimedes, and others. The medieval period, roughly spanning from the 5th to the late 15th centuries, saw a mix of continued study in geometry as well as the transmission of knowledge from the Islamic Golden Age.

Adam Friedrich Zürner (1630-1698) was a notable German mathematician and astronomer. He is particularly recognized for his work in the field of astronomical instruments and cartography, contributing to the understanding of celestial mechanics and the improvement of astronomical observations during the 17th century. Zürner is also known for publishing works that detailed his observations and findings, which were significant for the scientific community of his time.

Aida Yasuaki appears to be a lesser-known figure and not widely recognized in popular culture or media. It's possible that he could be a contemporary artist, a character in literature or film, or perhaps an emerging public figure in a specific field.

As of my last update in October 2023, Aissa Wade does not appear to be a widely recognized public figure, concept, or term. It's possible that it could refer to a specific individual, a character in a work of fiction, or a niche topic that hasn't gained significant attention.

Alan Weinstein is likely a reference to an accomplished mathematician and physicist known for his work in areas such as mathematics, theoretical physics, and particularly in relation to symplectic geometry.

Alexander Nabutovsky is known as a mathematician, specifically recognized for his work in the fields of topology and geometry. He has contributed to various areas of mathematical research, including the study of low-dimensional topology. His work often involves the examination of properties of manifolds and their relationships in different dimensions.

Anders Johan Lexell was a notable Swedish mathematician and astronomer, born on March 8, 1740, in Åbo, Finland, and he passed away on November 11, 1784. He is best known for his work in celestial mechanics and his contributions to the understanding of planetary motions. Lexell is particularly noted for developing Lexell's theorem concerning the perturbation of orbits, which is significant in the field of astronomy and the study of celestial bodies.

Anna Wienhard is a mathematician known for her contributions in the fields of geometry and topology, particularly in relation to Teichmüller theory, mathematical aspects of hyperbolic geometry, and geometric group theory. She has worked on various topics, including the study of discrete groups and their geometric actions on various spaces.