"Systems of Logic Based on Ordinals" refers to an area of mathematical logic that involves the use of ordinal numbers to develop systems of formal logical reasoning. This concept primarily revolves around the relationship between logic, computability, and set theory, particularly in the context of ordinal analysis and proof theory. ### Key Concepts: 1. **Ordinals**: Ordinal numbers generalize the concept of natural numbers to describe the order type of well-ordered sets.

The Takeuti–Feferman–Buchholz ordinal, often denoted by \( \Omega \), is a significant ordinal in the realm of proof theory and mathematical logic. It arises in the study of ordinal analysis of the system \( \text{PRA} \) (Primitive Recursive Arithmetic) and is particularly associated with the strength of formal systems and their consistency proofs.

Theories of iterated inductive definitions refer to a framework in the field of mathematical logic and computer science, particularly in the area of formal theories addressing the foundations of mathematics and computability. This framework involves defining sets or functions in a progressively layered or "iterated" manner, using rules of induction and often employing transfinite recursion. ### Key Concepts 1.

The Askey–Gasper inequality is a result in the field of mathematical analysis, particularly in the study of special functions and orthogonal polynomials. It provides bounds for certain types of sums and integrals involving orthogonal polynomials, especially within the context of Jacobi polynomials.

Fiction about origami can take many forms, blending the art of paper folding with various genres and themes. Here are a few ways origami is explored in fictional narratives: 1. **Magic and Fantasy**: In some stories, origami can be imbued with magical properties, where the folded paper creations come to life or possess mystical abilities. This could involve characters who use origami as a means of casting spells or communicating with spirits.

Discrete Chebyshev polynomials are a sequence of orthogonal polynomials defined on a discrete set of points, typically related to the Chebyshev polynomials of the first kind. These discrete polynomials arise in various applications, including numerical analysis, approximation theory, and computing discrete Fourier transforms. The discrete Chebyshev polynomials are defined based on the characteristic roots of the Chebyshev polynomials, which correspond to specific points on an interval.

Discrete orthogonal polynomials are a class of polynomials that are orthogonal with respect to a discrete measure or inner product. This means that they are specifically defined for sequences of points in a discrete set (often integers or specific values in the real line) rather than continuous intervals.

Dual Hahn polynomials are a class of orthogonal polynomials that arise in the context of approximation theory, special functions, and mathematical physics. They are part of a broader family of hypergeometric orthogonal polynomials and can be viewed as the dual version of Hahn polynomials.

Origami artists are individuals who practice the art of origami, which is the Japanese tradition of paper folding. This art form involves transforming a flat sheet of paper into a finished sculpture through folding techniques, without the use of cuts or glue. Origami artists can create a wide range of designs, from simple shapes like cranes and boats to complex structures that may require advanced techniques and multiple sheets of paper.

"Paper Planes" is a song by the British rapper M.I.A., released in 2008 as part of her album "Kala." The song became widely popular for its catchy chorus, which features the iconic sound of cash registers and gunshots, symbolizing themes of capitalism and violence. "Paper Planes" received critical acclaim and commercial success, charting in multiple countries and becoming a cultural touchstone.

Action origami is a branch of origami that emphasizes movement and mechanics in the folding process. Unlike traditional origami, which often focuses on static forms, action origami designs are created to perform specific motions or functions when manipulated. These designs can include flapping birds, popping boxes, and various toys or mechanical structures that exhibit movement, often requiring careful engineering to ensure functionality.

Akira Yoshizawa (1911-2005) was a renowned Japanese origami artist, often regarded as one of the most influential figures in the modern art of paper folding. He is credited with elevating origami from a traditional craft to a recognized art form, making significant contributions to the techniques and designs of origami. Yoshizawa developed a system of folding notation that allowed for the precise communication of complex origami designs.

Backcoating is a process used in the manufacturing of textiles and various types of materials, typically to enhance durability, moisture resistance, or other functional properties. It involves the application of a layer of material (often a polymer or adhesive) to the back side of a fabric or a substrate. This backing layer can provide several benefits: 1. **Increased Durability:** The backcoating can reinforce the base material, making it more resistant to wear and tear.

The British Origami Society (BOS) is an organization dedicated to promoting the art and craft of origami, the Japanese art of paper folding, in the United Kingdom. Established in 1967, the society aims to foster interest in origami, encourage creativity, and provide resources for both beginners and experienced folders. The society often organizes events, workshops, and conventions, and it publishes a magazine that features articles, designs, and tutorials related to origami.

"Bug Wars" could refer to different concepts depending on the context, such as a video game, educational tool, or a themed event. One notable context is a video game that involves strategy and simulation elements where players control various insect species to battle against each other. The gameplay often includes resource management, battling mechanics, and evolving species to gain strategic advantages.

A crease pattern is a specific arrangement of folds typically used in origami, paper engineering, and other forms of foldable structures. It is a two-dimensional diagram that represents all the creases needed to be made in a sheet of paper to create a particular three-dimensional shape or object. Crease patterns are often represented visually, showing both mountain folds (where the paper is folded upwards) and valley folds (where the paper is folded downwards).

Decorative folding is a creative technique that involves folding materials—such as paper, fabric, or other flexible mediums—into aesthetically pleasing shapes and forms. This technique is often used in various crafts, including origami, napkin folding, and fabric design. In the context of origami, decorative folding refers to the art of transforming a flat sheet of paper into intricate designs and sculptures through various folding techniques.

Origami, the art of paper folding, has a rich and intricate history that spans centuries and cultures. While the precise origins of origami are difficult to pinpoint, it is generally believed to have begun in China before spreading to Japan and other parts of the world. ### Early History: - **China (1st to 2nd Century AD)**: The earliest records of paper folding date back to China, where paper was invented around the 2nd century AD.

Kirigami is a traditional Japanese art form that involves the cutting and folding of paper to create intricate designs and three-dimensional shapes. The term "kirigami" derives from the Japanese words "kiri," meaning "to cut," and "gami," meaning "paper." While it is similar to origami, which focuses on folding paper without cuts, kirigami includes both cutting and folding techniques, allowing for more complex and decorative creations.

A list of origamists would typically include individuals known for their contributions to the art of origami, either as artists, designers, or scholars. These origamists may be famous for creating original designs, developing new techniques, or promoting the art of paper folding through education and workshops.