The Lénárt sphere is a physical representation of the celestial sphere used primarily in the field of astronomy and navigation. It is a spherical model that helps visualize the positions of stars, planets, and other celestial objects in relation to Earth. The design incorporates a scale that allows users to represent the apparent movement of celestial bodies across the sky during different times of the year.

A Casson handle is a mathematical concept used in the field of 3-manifold topology, specifically in the study of 3-manifolds and their structures. To understand what a Casson handle is, it's essential to first understand its role in manifolds and handle decompositions. In topology, a *handle* is a basic building block used to construct manifolds.

A dodecahedral bipyramid is a polyhedron formed by connecting two regular dodecahedra (which are 12-faced polyhedra with regular pentagonal faces) at their bases. It can also be viewed as a bipyramid with a dodecahedron as its base, which consists of 12 pentagonal faces.

An octahedral pyramid is a three-dimensional geometric figure formed by extending the apex (top point) of a pyramid to the center of an octahedron. An octahedron itself is a polyhedron composed of eight triangular faces.

D-Orbit is an Italian aerospace company that specializes in satellite transportation and orbital services. Founded in 2011, the company focuses on providing innovative solutions for satellite deployment and end-of-life management through its flagship product, the ION Satellite Carrier. This satellite platform is designed to deploy multiple payloads to specific orbits, facilitating rideshare missions and increasing the efficiency of satellite launches.

Kostant's convexity theorem is a result in the field of representation theory and geometry, specifically relating to the representation of Lie groups and the geometry of their associated symmetric spaces. The theorem is named after Bertram Kostant, who made significant contributions to these areas. In essence, Kostant's convexity theorem states that for a compact Lie group \( G \) and a certain class of representations, the image of the highest weight map is a convex polytope in the weight space.

The Bass conjecture is a conjecture in algebraic K-theory, specifically concerning the K-theory of integral domains and, more generally, rings. It was proposed by Hyman Bass in the 1960s.

Homography is a concept from projective geometry that describes a specific type of transformation between two planes. In the context of computer vision and image processing, homography is often used to relate the coordinates of points in one image to the coordinates of points in another image, typically when those images are of the same scene from different perspectives. ### Mathematical Definition Mathematically, a homography can be represented by a \(3 \times 3\) matrix \(H\).

The Nakai conjecture is a concept in the field of algebraic geometry, specifically related to the theory of ample and pseudoeffective line bundles.

Egyptian geometry refers to the mathematical practices and concepts used by ancient Egyptians, particularly during the early periods of their civilization, around 3000 BCE to 300 BCE. The Egyptians developed a practical approach to geometry primarily for the purposes of land measurement, construction, astronomy, and agriculture.

In geometry, "quadrature" refers to the process of determining the area of a geometric shape, especially when that area cannot be easily calculated using standard formulas. Historically, this term has been used in the context of finding the area of a square that is equivalent in area to a given shape or curve, such as a circle. This concept originates from the Latin word "quadratus," which means "square.

The complex projective plane, denoted as \(\mathbb{CP}^2\), is a fundamental object in complex geometry and algebraic geometry. It can be understood as a two-dimensional projective space over the field of complex numbers \(\mathbb{C}\).

The term "imaginary curve" can refer to different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Complex Analysis**: In the field of mathematics, particularly in complex analysis, an imaginary curve might refer to a curve defined by complex numbers. Complex numbers can be expressed in the form \( z = x + iy \), where \( x \) and \( y \) are real numbers, and \( i \) is the imaginary unit.

A Möbius transformation (or linear fractional transformation) is a function defined on the complex numbers that has the general form: \[ f(z) = \frac{az + b}{cz + d} \] where \(a\), \(b\), \(c\), and \(d\) are complex numbers, and \(ad - bc \neq 0\) to ensure that the transformation is well-defined (i.e., it is not degenerate).

In projective geometry, a **spread** refers to a specific type of geometric configuration. More formally, a spread of a projective space is a set of lines such that any two lines in the set intersect in a single point—essentially, it is a collection of lines that are pairwise distinct but share points as intersections. To provide a further context, consider a projective space over a division ring.

The aerospace industry is a global sector, and businesspeople within it come from various nationalities. Here's an overview of significant countries involved in aerospace and some key players by nationality: 1. **United States**: - Major companies include Boeing, Lockheed Martin, Northrop Grumman, and Raytheon. Many prominent aerospace executives and business leaders are American.