The proof of the four color theorem is also noteworthy for being the first major computer-aided proof.

In this period Heesch did pioneer work in developing methods for a computer-aided proof of the then unproved Four color theorem.

In particular, he was the first to investigate the notion of " discharging ", which turned out to be a fundamental ingredient of the eventual computer-aided proof by Kenneth Appel and Wolfgang Haken.

This became known as the Four Color Problem, and remained one of the most famous unsolved problems in topology for more than a century, until it was eventually proven in 1976 using a controversial computer-aided proof which was lengthy and inelegant.

American mathematician Thomas Callister Hales has given a computer-aided proof of the Kepler conjecture.

Music produced with notation or sequencing software could easily be considered computer-aided composition.

The photomask is usually prepared with a photoplotter from data produced by a technician using CAM, or computer-aided manufacturing software.

The use of computer-aided shaping, combined with radar-absorbent materials, produced aircraft of drastically reduced radar cross section ( RCS ) that were much more difficult to detect on radar.

With transcripts produced on computer-aided transcription ( CAT ) software, a scopist no longer needs to have any knowledge of shorthand theories because the software converts shorthand to English in real time, via a dictionary.

Similarly, the design technique has progressed from paper-and-ruler based manual design to computer-aided design, and now to computer-automated design ( CAutoD ), which has been made possible by evolutionary computation.

In the computer science subfields of computer-aided design and computer graphics, the term B-spline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of B-splines ( in the mathematical sense above ).

Demonstrations of the first commercial application for X ( a mechanical computer-aided engineering system from Cognition Inc. that ran on VAXes and remotely displayed on PCs running an X server ported by Jim Fulton and Jan Hardenbergh ) took place at the Autofact trade show at that time.

Pro / ENGINEER ( as well as other commercial computer-aided design ( CAD ) programs ) does however hold the possibility to create top-down design by the use of so-called skeletons.

ACIS is used by many software developers in industries such as computer-aided design ( CAD ), Computer-aided manufacturing ( CAM ), Computer-aided engineering ( CAE ), Architecture, engineering and construction ( AEC ), Coordinate-measuring machine ( CMM ), 3D animation, and shipbuilding.

QLISP was used by Richard Waldinger and Karl Levitt for program verification, by Earl Sacerdoti for planning and execution monitoring, by Jean-Claude Latombe for computer-aided design, by Richard Fikes for deductive retrieval, and by Steven Coles for an early expert system that guided use of an econometric model.

Once targets are identified, candidate drugs can be selected, either from drugs already known to have appropriate effects, or by actually designing the candidate at the molecular level with a computer-aided design program.

The file specification was introduced by Esri .< ref > Esri also has another world file format that applies to computer-aided design or CAD drawing files.

Character-by-character, computer-aided phototypesetting was, in turn, rapidly rendered obsolete in the 1980s by fully digital systems employing a raster image processor to render an entire page to a single high-resolution digital image, now known as imagesetting.

In MBD, the information captured by the CAD software app is fed automatically into a CAM app ( computer-aided manufacturing ), and is translated via postprocessor into other languages such as G-code, which is executed by a CNC machine tool ( computer numerical control ).

Mastercam's name is a double entendre: it implies mastery of CAM ( computer-aided manufacturing ), which involves today's latest machine tool control technology ; and it simultaneously pays homage to yesterday's machine tool control technology by echoing the older term master cam, which referred to the main cam or model that a tracer followed in order to control the movements of a mechanically automated machine tool.

In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces and edges constitute a continuous boundary of a 3D body.

During the 1980s and 1990s, computer-aided prepress techniques began to supplant the traditional dark room and light table processes, and by the early 2000s the word prepress became, in some ways, synonymous with digital prepress.

In the study by Krus and Hoehl, variables that might explain differences in incarceration rates among populations were located by a computer-aided search of the compendium of world rankings, compiled by the Facts on File Corporation and the World Model Group, containing over 50, 000 records on more than 200 countries.

Developed and manufactured by Silicon Graphics Incorporated ( SGI ), it was the result of their attempt to obtain a share of the low-end computer-aided design ( CAD ) market, which was dominated at the time by other workstation vendors ; and the desktop publishing and multimedia markets, which were mostly dominated at the time by Apple Computer.

Today most engineering work involves the use of computers and it is commonplace to use computer-aided design programs when designing electrical systems.

Computer-aided design ( CAD ), also known as computer-aided design and drafting ( CADD ), is the use of computer systems to assist in the creation, modification, analysis, or optimization of a design.

Therapists develop computer-aided adaptive equipment and teach clients with severe limitations how to use that equipment in order to communicate better and control various aspects of their environment.

Today, the mechanics of the drafting task have largely been automated and accelerated through the use of computer-aided design systems ( CAD ).

Popular IBM PC programs at the time ( such as Lotus 1-2-3 spreadsheet and Autocad computer-aided drafting ) came with their own drivers to allow use of the Hercules graphics mode.

Professional LDs generally use special computer-aided design packages to create accurate and easily readable drafted plots that can be swiftly updated as necessary.

During the 1970s the combined AISI Committees of Structural Steel Producers and Steel Plate Producers engaged in a series of research and promotional seminars and publication programs that focused, for example, on the use of steel storage tanks and transmission pipage in the water utility business, innovations in computer-aided design for structural steel frames for high-rise and arena buildings, applications for structural and steel plate in new mass transit system designs, and in utility poles for high voltage electrical transmission systems.

Mass customization, in marketing, manufacturing, call centres and management, is the use of flexible computer-aided manufacturing systems to produce custom output.

Modern computer-aided drafting ( CAD ) systems use vector-based graphics to achieve a precise radius, so no template is required.

The modern hydraulic engineer uses the same kinds of computer-aided design ( CAD ) tools as many of the other engineering disciplines while also making use of technologies like computational fluid dynamics to perform the calculations to accurately predict flow characteristics, GPS mapping to assist in locating the best paths for installing a system and laser-based surveying tools to aid in the actual construction of a system.

Once components are manufactured their geometrical form and size can be checked against the original CAD data with the use of computer-aided inspection equipment and software.

Prior to the widespread use of the Internet, Nadin developed several computer-aided educational aids.

He is distinguished for his use of computer-aided design to produce irregular, biomorphic architectural forms, as he proposes that with the use of computers, calculus can be implemented into the generation of architectural expression.

With the use of computer-aided communication devices, readers get to see only a glimpse of barast language.

SolidWorks is a 3D mechanical CAD ( computer-aided design ) program that runs on Microsoft Windows and is being developed by Dassault Systèmes SolidWorks Corp., a subsidiary of Dassault Systèmes, S. A.

Consequently, Group Systems was developed as a tool for the expert facilitator of computer-aided meetings.

Harris's methodology was developed into a system for the computer-aided analysis of natural language by a team led by Naomi Sager at NYU, which has been applied to a number of sublanguage domains, most notably to medical informatics.

ADA has developed specialized software in the fields of computer-aided design ( CAD ), computer-aided engineering ( CAE ), computer-aided manufacturing ( CAM ), avionics, systems, independent validation and verification, flight simulation.

In the mid 1900s F. Freudenstein and G. N. Sandor used the newly developed digital computer to solve the loop equations of a linkage and determine its dimensions for a desired function, initiating the computer-aided design of linkages.

Vectorworks is a computer-aided design ( CAD ) and Building Information Modeling ( BIM ) software program developed by Nemetschek Vectorworks that is used for drafting, technical drawing and 3D modeling.

In particular, he formulated a relatively fast and numerically stable algorithm for calculating the values of splines ( used extensively in computer-aided design and computer graphics ), and advocated for the formulation of spline functions in terms of the basis splines, or B-splines developed by Schoenberg and Curry.

DataCAD is a computer-aided design and drafting ( CADD ) software for 2D and 3D architectural design and drafting, developed and sold by DATACAD LLC.

Laser engineered net shaping or LENS is a technology developed by Sandia National Laboratories for fabricating metal parts directly from a computer-aided design ( CAD ) solid model by using a metal powder injected into a molten pool created by a focused, high-powered laser beam.