Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
Proof assistantIn computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Euler characteristicIn mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by (Greek lower-case letter chi). The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids.
Cone cellCone cells, or cones, are photoreceptor cells in the retinas of vertebrates' eyes, including the human eye. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. Cones function best in relatively bright light, called the photopic region, as opposed to rod cells, which work better in dim light, or the scotopic region. Cone cells are densely packed in the fovea centralis, a 0.
Cone dystrophyA cone dystrophy is an inherited ocular disorder characterized by the loss of cone cells, the photoreceptors responsible for both central and color vision. The most common symptoms of cone dystrophy are vision loss (age of onset ranging from the late teens to the sixties), sensitivity to bright lights, and poor color vision. Therefore, patients see better at dusk. Visual acuity usually deteriorates gradually, but it can deteriorate rapidly to 20/200; later, in more severe cases, it drops to "counting fingers" vision.
Uniform star polyhedronIn geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can contain either star polygon faces, star polygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the 4 regular ones, called the Kepler–Poinsot polyhedra, 5 quasiregular ones, and 48 semiregular ones. There are also two infinite sets of uniform star prisms and uniform star antiprisms.
PolyhedronIn geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.
Grading in educationGrading in education is the process of applying standardized measurements for varying levels of achievements in a course. Grades can be assigned as letters (usually A through F), as a range (for example, 1 to 6), as a percentage, or as a number out of a possible total (often out of 100). In some countries, grades are averaged to create a grade point average (GPA). GPA is calculated by using the number of grade points a student earns in a given period of time.
Grading (tumors)In pathology, grading is a measure of the cell appearance in tumors and other neoplasms. Some pathology grading systems apply only to malignant neoplasms (cancer); others apply also to benign neoplasms. The neoplastic grading is a measure of cell anaplasia (reversion of differentiation) in the sampled tumor and is based on the resemblance of the tumor to the tissue of origin. Grading in cancer is distinguished from staging, which is a measure of the extent to which the cancer has spread.
Semiregular polyhedronIn geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on its vertices; today, this is more commonly referred to as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope). These polyhedra include: The thirteen Archimedean solids.
Star polyhedronIn geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general kinds of star polyhedron: Polyhedra which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way. Mathematically these figures are examples of star domains. Mathematical studies of star polyhedra are usually concerned with regular, uniform polyhedra, or the duals of the uniform polyhedra.
