Pythagorean symbols refer to a system of symbols and concepts linked to the Pythagorean school of thought, associated with the ancient Greek philosopher Pythagoras and his followers. While often discussed in the context of mathematics—especially the Pythagorean theorem relating to right triangles—these symbols can also pertain to broader spiritual and philosophical ideas.

Fold equity is a concept in poker that refers to the potential value a player gains by making an opponent fold their hand. It is an essential part of evaluating the profitability of a bluff or semi-bluff. When a player bets or raises, they not only rely on their own hand strength to win the pot but also on the possibility that their opponent will fold, thus not allowing the hand to progress to a showdown.

An augmented triangular prism is a three-dimensional geometric shape that is created by adding a pyramid-like structure (often referred to as an "augmentation") to one of the triangular faces of a triangular prism. A triangular prism itself consists of two parallel triangular bases connected by three rectangular lateral faces. When you augment one of the triangular bases, you typically create a new face that extends out from the base, adding volume and complexity to the shape.

The compound of five nonconvex great rhombicuboctahedra is a fascinating arrangement in the field of geometry, specifically in the study of polyhedra and their combinations. The great rhombicuboctahedron is a nonconvex Archimedean solid, composed of 8 square and 24 triangular faces, and has some interesting properties related to symmetry and vertex arrangement.

A compound of six pentagrammic prisms refers to a polyhedral structure formed by combining six pentagrammic prisms. A pentagrammic prism itself is a three-dimensional geometric shape that has two pentagram (five-pointed star) bases connected by rectangular lateral faces. When multiple pentagrammic prisms are combined into a compound, they share spatial relationships and may intersect or connect in various ways.

A decagrammic prism is a type of polyhedron characterized by its decagrammic base and straight, vertical sides. 1. **Base Shape**: The term "decagrammic" refers to a 10-sided star polygon, often constructed by connecting every second vertex of a regular decagon (10-sided polygon).

The compound of twelve pentagonal antiprisms with rotational freedom refers to a complex geometric structure that consists of twelve pentagonal antiprisms arranged in a way that allows for rotational movement. A pentagonal antiprism is a polyhedron with two parallel pentagonal bases and ten triangular lateral faces. In this compound, each antiprism can rotate around its central axis, creating a dynamic interaction between the antiprisms.

The compound of two truncated tetrahedra forms a polyhedral structure that is intriguing in both geometry and topology. A truncated tetrahedron, which is one of the Archimedean solids, is created by truncating (slicing off) the corners (vertices) of a regular tetrahedron, resulting in a solid with 4 triangular faces and 4 hexagonal faces.

The elongated pentagonal orthobicupola is a type of convex polyhedron and is part of the family of Archimedean solids. It is characterized by its unique geometry, which combines elements of both pentagonal and triangular figures.

The elongated square cupola is a type of Archimedean solid, which is a category of convex polyhedra with regular polygons as their faces. Specifically, the elongated square cupola can be described as follows: - **Vertices**: It has a total of 20 vertices. - **Edges**: There are 30 edges. - **Faces**: The solid comprises 10 faces: 4 square faces and 6 triangular faces.

An enneagonal prism is a three-dimensional geometric shape that is categorized as a prism. Specifically, it has two bases that are enneagons, which are nine-sided polygons. Here are some characteristics of an enneagonal prism: 1. **Bases**: The two parallel bases are both enneagons, meaning each base has nine sides and nine angles. 2. **Lateral Faces**: The lateral faces of the prism are rectangles.

"Asian mathematician stubs" typically refers to short articles or entries on Wikipedia that pertain to mathematicians from Asian countries. The term "stub" in the context of Wikipedia indicates that the article is incomplete and likely requires additional information, references, or expansion to provide a more comprehensive overview of the subject. These stubs allow contributors to identify areas where they can help improve Wikipedia by adding content about notable Asian mathematicians, their contributions, biographical details, and other relevant information.

"Mathematicians from Philadelphia" typically refers to a notable group of mathematicians associated with the Philadelphia area, particularly those who have made significant contributions to various fields of mathematics. Some prominent mathematicians who are known to have worked in Philadelphia or have ties to institutions there include: 1. **John von Neumann** - Although primarily associated with several other cities, his involvement in the early days of computer science and game theory has connections to Philadelphia through his work with the Institute for Advanced Study.

The Clay Research Award is given by the Clay Mathematics Institute to recognize outstanding achievements in mathematics. This award is intended to honor mathematicians for their significant contributions to the field, particularly those who have made groundbreaking advances or provided important insights into mathematical problems. Recipients of the Clay Research Award are typically selected based on their work's originality, depth, and impact on the mathematical community. The awards serve not only to recognize individual researchers but also to promote mathematics as a whole.

The Fields Medal is one of the most prestigious awards in mathematics, often regarded as the equivalent of a Nobel Prize for mathematicians. It was established in 1936 and is awarded every four years to mathematicians under the age of 40 in recognition of outstanding achievements in the field. The award was named after Canadian mathematician John Charles Fields, who was instrumental in establishing the medal and the associated prize.