Please answer this: Information:  - A programming language is a formal computer language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs to control the behavior of a machine or to express algorithms.  - .NET Framework (pronounced "dot net") is a software framework developed by Microsoft that runs primarily on Microsoft Windows. It includes a large class library known as Framework Class Library (FCL) and provides language interoperability (each language can use code written in other languages) across several programming languages. Programs written for .NET Framework execute in a software environment (in contrast to a hardware environment) known as Common Language Runtime (CLR), an application virtual machine that provides services such as security, memory management, and exception handling. (As such, computer code written using .NET Framework is called "managed code".) FCL and CLR together constitute .NET Framework.  - Prolog is a general-purpose logic programming language associated with artificial intelligence and computational linguistics.  - Computational linguistics is an interdisciplinary field concerned with the statistical or rule-based modeling of natural language from a computational perspective.  - Logic programming is a type of programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic programming language families include Prolog, Answer set programming (ASP) and Datalog. In all of these languages, rules are written in the form of "clauses":  - Artificial intelligence (AI) is intelligence exhibited by machines. In computer science, an ideal "intelligent" machine is a flexible rational agent that perceives its environment and takes actions that maximize its chance of success at some goal. Colloquially, the term "artificial intelligence" is applied when a machine mimics "cognitive" functions that humans associate with other human minds, such as "learning" and "problem solving". As machines become increasingly capable, mental facilities once thought to require intelligence are removed from the definition. For example, optical character recognition is no longer perceived as an exemplar of "artificial intelligence", having become a routine technology. Capabilities currently classified as AI include successfully understanding human speech, competing at a high level in strategic game systems (such as Chess and Go), self-driving cars, and interpreting complex data. Some people also consider AI a danger to humanity if it progresses unabatedly.  - The Common Language Infrastructure (CLI) is an open specification (technical standard) developed by Microsoft and standardized by ISO and ECMA that describes executable code and a runtime environment that allows multiple high-level languages to be used on different computer platforms without being rewritten for specific architectures. This implies it is platform agnostic. The .NET Framework and the free and open source Mono and Portable.NET are implementations of the CLI.  - Part of the decommissioned DotGNU project, Portable.NET is a free software and open source software initiative aiming to build a portable toolchain and runtime for Common Language Infrastructure applications. The project focuses on compatibility with the ECMA-334 and ECMA-335 standards and support for .NET's base class libraries, XML, and Windows Forms. the latest release of Portable.NET is 0.8.0. The project supports a number of different CPU architectures and operating systems.  - Microsoft Corporation (commonly referred to as Microsoft or MS) is an American multinational technology company headquartered in Redmond, Washington, that develops, manufactures, licenses, supports and sells computer software, consumer electronics and personal computers and services. Its best known software products are the Microsoft Windows line of operating systems, Microsoft Office office suite, and Internet Explorer and Edge web browsers. Its flagship hardware products are the Xbox video game consoles and the Microsoft Surface tablet lineup. As of 2016, it was the world's largest software maker by revenue, and one of the world's most valuable companies.  - P # is a Prolog interpreter written for the Common Language Infrastructure . Features : Languages extensions allow concurrency in Prolog . Prolog programs can create any .NET object . Compatible with Microsoft .NET Framework and Mono .    What is the relationship between 'p sharp' and 'programming language'?
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Answer: instance of


Please answer this: Information:  - A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The th triangular number is the number of dots composing a triangle with dots on a side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is  - In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers.  - The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean  - A hexagonal number is a figurate number . The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots , when the hexagons are overlaid so that they share one vertex . The formula for the nth hexagonal number h_n = 2n ^ 2 - n = n ( 2n - 1 ) = ( ( 2n ) \ times ( ( 2n - 1 ) ) \ over 2 ) . \ , \ ! The first few hexagonal numbers ( sequence A000384 in OEIS ) are : 1 , 6 , 15 , 28 , 45 , 66 , 91 , 120 , 153 , 190 , 231 , 276 , 325 , 378 , 435 , 496 , 561 , 630 , 703 , 780 , 861 , 946 . Every hexagonal number is a triangular number , but only every other triangular number ( the 1st , 3rd , 5th , 7th , etc. ) is a hexagonal number . Like a triangular number , the digital root in base 10 of a hexagonal number can only be 1 , 3 , 6 , or 9 . The digital root pattern , repeating every nine terms , is `` 1 6 6 1 9 3 1 3 9 '' . Every even perfect number is hexagonal , given by the formula M_p 2 ^ ( p - 1 ) = M_p ( M_p + 1 ) / 2 = h -- ( ( M_p +1 ) / 2 ) = h -- ( 2 ^ ( p - 1 ) ) where Mp is a Mersenne prime . No odd perfect numbers are known , hence all known perfect numbers are hexagonal . For example , the 2nd hexagonal number is 2 × 3 = 6 ; the 4th is 4 × 7 = 28 ; the 16th is 16 × 31 = 496 ; and the 64th is 64 × 127 = 8128 . The largest number that can not be written as a sum of at most four hexagonal numbers is 130 . Adrien - Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this way . Hexagonal numbers can be rearranged into rectangular numbers of size n by ( 2n  1 ) . Hexagonal numbers should not be confused with centered hexagonal numbers , which model the standard packaging of Vienna sausages . To avoid ambiguity , hexagonal numbers are sometimes called `` cornered hexagonal numbers '' .    What is the relationship between 'hexagonal number' and 'polygonal number'?
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Answer:
subclass of