Frederick Purser may refer to several individuals, but he is most widely recognized as an Irish politician and a member of the British Parliament during the late 19th and early 20th centuries. He served as a member of the Irish Parliamentary Party and was known for advocating for Irish rights and home rule.

Jean Paul de Gua de Malves was a French mathematician known for his work in the field of geometry and for his contributions to the study of infinitesimal calculus. He was born in the late 17th century, around 1730, and passed away in 1788. Gua de Malves is best known for his developments in the area of differential geometry and for his work on the principles of mathematical analysis.

Pierre de Fermat (1601–1665) was a French lawyer and mathematician who is best known for his contributions to number theory and for Fermat's Last Theorem. Although he was not a professional mathematician and did not publish his work in the way that many of his contemporaries did, his insights and writings laid important groundwork for modern mathematics.

János Bolyai (1802–1860) was a Hungarian mathematician known for his foundational work in non-Euclidean geometry. He is best known for developing the principles of hyperbolic geometry independently of the Russian mathematician Nikolai Lobachevsky. Bolyai's work demonstrated that it is possible to construct a consistent geometric system in which the parallel postulate of Euclidean geometry does not hold.

Qāḍī Zāda al-Rūmī, also known simply as Qāḍī Zāda, was a notable figure in the realm of Islamic scholarship and science during the late medieval period, specifically in the 15th century. He was born in 1364 in the city of Edirne (Adrianople) in present-day Turkey and is esteemed for his contributions to mathematics, astronomy, and various Islamic sciences.

The Hilbert curve is a continuous fractal space-filling curve that maps a one-dimensional interval (like the interval [0, 1]) onto a multi-dimensional space, typically a square or cube. It was first proposed by the German mathematician David Hilbert in 1891. The curve is constructed recursively, starting from a simple shape and progressively refining it.

The Hasse–Minkowski theorem is a result in the field of number theory, specifically concerning the theory of quadratic forms. It establishes a fundamental connection between the local and global solvability of quadratic forms over the rational numbers. In simple terms, the theorem states that a quadratic form over the rational numbers can be represented by integers if and only if it can be represented by integers when considered over the completions of the rational numbers at all finite places and at infinity (the real numbers).

The Minkowski–Bouligand dimension, also known as the box-counting dimension, is a concept in fractal geometry that provides a way to measure the dimensionality of a set in a more general sense than traditional Euclidean dimensions. It is particularly useful for non-integer dimensions, which often arise in fractals and irregular geometric shapes.

Fractals are complex geometric shapes that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self-similarity. Fractals can be found in mathematics, but they also appear in nature and other fields such as computer graphics, art, and even economics. ### Key Characteristics of Fractals: 1. **Self-Similarity**: Fractals display patterns that repeat at different scales.

An Archimedean circle is not a standard mathematical term, but it might refer to concepts related to Archimedes and circles in geometry. Archimedes of Syracuse, an ancient Greek mathematician, made significant contributions to the understanding of circles and geometry. One of his famous works involves the relationship between the circumference and diameter of a circle, leading to the approximation of π (pi).

Coinage shapes refer to the distinct geometrical forms and designs of coins, which can vary based on cultural, historical, and practical considerations. Here are the main aspects related to coinage shapes: 1. **Physical Shape**: The most common shape for coins is round, but coins can also be found in various other shapes such as polygonal, square, or even irregular forms. The shape can be influenced by technological and minting capabilities, as well as aesthetic choices.

"Fusiform" is an adjective used in various contexts, typically meaning "spindle-shaped" or "tapering at both ends." The term can describe objects or structures that are wider in the middle and tapered at both ends, similar to the shape of a spindle. In anatomy, "fusiform" often refers to specific shapes of muscles or cells.

A glossary of shapes with metaphorical names typically includes terms that describe geometric shapes while also conveying deeper meanings, concepts, or associations. Below are some common shapes and their metaphorical interpretations: 1. **Circle** - Represents unity, wholeness, and infinity. It often symbolizes continuity and the cyclical nature of life.

In geometry, a "lemon" refers to a specific type of concave polygon that resembles the shape of a lemon. It is characterized by being a balanced shape with one distinct concave region. In a lemon shape, the boundary typically has a "cusp" or point where the interior angles are greater than 180 degrees, giving it a concave appearance. The lemon shape is often studied in the context of various mathematical properties, including its area, perimeter, and applications in geometric problems.

The medial axis of a shape is a concept from computational geometry that represents a set of points equidistant from the nearest boundary points of the shape. In simpler terms, it can be thought of as the "skeleton" or "centerline" of a shape, capturing the essential structure while simplifying its geometry. Mathematically, the medial axis can be defined as the locus of all points where there exists at least one closest point on the boundary of the shape.

Parbelos, also known as "Tarbelos," refers to a concept in mathematics, particularly in the field of geometry. It is associated with a specific type of mathematical figure or geometric construct, often related to problems involving curves and areas. However, the term may not be widely recognized, and it can vary depending on the context.

A sphericon is a geometric shape that resembles a combination of a sphere and a cone. It is formed by taking a solid, known as a sphericon, which is created by rotating a certain shape (typically a triangular section) about an axis that is not aligned with its base. The sphericon has a unique property: it can roll smoothly in any direction on a flat surface, which is a characteristic that distinguishes it from traditional cones.

A surface of constant width is a geometric shape in three-dimensional space such that any two parallel planes that intersect the surface have the same distance between them, regardless of the orientation of the planes. In other words, the distance between parallel tangents to the surface is constant, serving as a uniform measure of width. One of the classic examples of a surface of constant width is the **sphere**, where the distance between any two parallel planes that touch the sphere is equal to the diameter of the sphere.

"Ungula" is a term that can refer to various contexts depending on the field: 1. **Biology and Zoology**: In biological terms, "ungula" is derived from Latin and refers to a hoof or a claw. It can be used to describe the hooves of ungulates, which are a group of large mammals that includes animals like horses, cows, and deer.

The Brascamp–Lieb inequality is an important result in the field of functional analysis and geometric measure theory. It provides a powerful estimate for integrals of products of functions that arise in various areas of mathematics, including harmonic analysis and the theory of partial differential equations. ### Statement of the Inequality The Brascamp–Lieb inequality states that for a collection of measurable functions and linear maps, one can obtain an upper bound on the integral of a product of these functions.