Conic sections, or conics, are the curves obtained by intersecting a right circular cone with a plane. The type of curve produced depends on the angle at which the plane intersects the cone. There are four primary types of conic sections: 1. **Circle**: Formed when the intersecting plane is perpendicular to the axis of the cone. A circle is the set of all points that are equidistant from a fixed center point.

"Destroyers II" is likely a reference to a type of video game, specifically a casual game or a shooter game. However, as of my last knowledge update in October 2023, there is no widely known game called "Destroyers II." It's possible that it could be a sequel to a game called "Destroyers" or a similar title.

Super envy-freeness is a concept in the field of fair division, which is a branch of mathematics and economics focused on how to divide resources among several parties in a way that is considered fair. In traditional envy-freeness, a division of goods is considered envy-free if no individual prefers another individual's allocation over their own. In other words, each person feels satisfied with what they have, such that they do not envy anyone else's share.

Cake Theory, often referred to in the context of economics and social sciences, is a metaphor used to illustrate the complexities of resource distribution and allocation among different entities, such as individuals or groups. The concept can be exemplified through various scenarios where a "cake" represents a limited resource that is to be divided among parties with possibly conflicting interests.

The moving-knife procedure is a method used in economics, particularly in the context of fair division problems. It is a way to allocate resources or goods among individuals in a manner that is considered fair based on their preferences. The method is often applied in situations where indivisible goods are involved, or where parties have different valuations of the items being divided.

Proportional cake-cutting refers to a method of fairly dividing a resource—often represented as a "cake"—among multiple parties (or "players"), such that each player receives a piece they consider to be at least a certain fraction of the total value of the cake. The aim is to ensure that each participant is satisfied with their share and feels that it is a fair division according to their own preferences.

The "price of fairness" is a concept derived from economics and game theory that refers to the potential costs that individuals or groups incur when they prioritize fairness or equity in decision-making processes over their own self-interest or the most efficient outcomes. In various scenarios, particularly in negotiations, business settings, or resource allocation, the pursuit of fairness can lead to suboptimal results or inefficiencies.

The term "house rule" can refer to different concepts depending on the context: 1. **In Gaming**: House rules are informal rules adopted by a group of players that modify or replace the official rules of a game. These rules can help tailor the game experience to better fit the preferences of the group, addressing specific issues or enhancing enjoyment.

The term "lusory attitude" refers to the mindset or approach that individuals adopt when engaging in games or play. It was popularized by philosopher Bernard Suits in his work on the philosophy of games. The lusory attitude involves accepting the rules of a game and pursuing the goals defined by those rules, all while acknowledging that these rules may be artificial or arbitrary. In essence, the lusory attitude allows players to immerse themselves in a game despite knowing that the game's context is separate from reality.

A coordinate system is a mathematical framework used to define the position of points in a space. It allows for the representation of geometric objects and their relationships in a consistent way. Depending on the dimensionality of the space, different types of coordinate systems can be used.

Helmholtz decomposition is a theorem in vector calculus that states that any sufficiently smooth, rapidly decaying vector field in three-dimensional space can be uniquely expressed as the sum of two components: a gradient of a scalar potential (irrotational part) and the curl of a vector potential (solenoidal part).

Spherical geometry is a branch of mathematics that deals with geometric shapes and figures on the surface of a sphere, as opposed to the flat surfaces typically studied in Euclidean geometry. It is a non-Euclidean geometry, meaning that it does not abide by some of the postulates of Euclidean geometry, particularly the parallel postulate.

Pappus of Alexandria was a Greek mathematician who lived during the 4th century AD, in the Roman province of Egypt. He is best known for his work "Collection," a compendium of Greek mathematics that preserves and elaborates on the contributions of earlier mathematicians, particularly in the fields of geometry and number theory. Pappus's "Collection" is divided into several books, discussing various topics such as projective geometry, mechanics, and mathematical theory.

Bjorn Poonen is a mathematician known for his work in number theory, especially in the areas of arithmetic geometry, algebraic geometry, and the arithmetic of elliptic curves. He has contributed to various advances in the understanding of rational points on algebraic varieties and has worked on topics related to the Birch and Swinnerton-Dyer conjecture, an important conjecture in number theory that connects the number of rational points on an elliptic curve to the behavior of an associated L-function.

Pietro Corvaja is not a widely recognized public figure, concept, or term as of my last knowledge update in October 2023. It is possible that he may be a private individual or someone who has gained notoriety after that time.

Harold Scott MacDonald Coxeter (1907–2003) was a prominent British mathematician known for his work in the field of geometry, particularly in the study of polytopes, tessellations, and higher-dimensional spaces. He made significant contributions to several areas of mathematics, including topology and group theory. Coxeter is perhaps best known for his research on regular polytopes and the classification of geometric figures in various dimensions.

Peter McMullen could refer to different individuals depending on the context. One well-known Peter McMullen is a British scientist recognized for his work in mathematics, particularly in the field of topology and geometric group theory. He might also be associated with various other fields or industries. Without more specific context, it’s difficult to pinpoint exactly which Peter McMullen you are referring to.

Alicia Boole Stott was an Irish mathematician known for her work in geometry and her contributions to the field of mathematics during the late 19th and early 20th centuries. Born in 1860 in Dublin, Ireland, she made significant advancements in the study of higher-dimensional polytopes and was particularly interested in the geometry of four-dimensional spaces. Stott is best known for her work in the visualization of complex geometric figures, including the regular polytopes in four dimensions.

Christiaan Huygens (1629–1695) was a Dutch mathematician, physicist, and astronomer who made significant contributions to various fields of science. He is best known for his work in optics, mechanics, and the study of celestial bodies. Some of Huygens' notable achievements include: 1. **Wave Theory of Light**: Huygens proposed that light behaves as a wave rather than as a particle, a revolutionary idea at the time.