Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.
Research is "creative and systematic work undertaken to increase the stock of knowledge, including knowledge of humans, culture and society, and the use of this stock of knowledge to devise new applications." It is used to establish or confirm facts, reaffirm the results of previous work, solve new or existing problems, support theorems, or develop new theories. A research project may also be an expansion on past work in the field. Research projects can be used to develop further knowledge on a topic, or in the example of a school research project, they can be used to further a student's research prowess to prepare them for future jobs or reports. To test the validity of instruments, procedures, or experiments, research may replicate elements of prior projects or the project as a whole. The primary purposes of basic research are documentation, discovery, interpretation, or the research and development (R&D) of methods and systems for the advancement of human knowledge. Approaches to research depend on epistemologies, which vary considerably both within and between humanities and sciences. There are several forms of research: scientific, humanities, artistic, economic, social, business, marketing, practitioner research, life, technological, etc. The scientific study of research practices is known as meta-research.
Geomorphology is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or near the Earth's surface. Geomorphologists seek to understand why landscapes look the way they do, to understand landform history and dynamics and to predict changes through a combination of field observations, physical experiments and numerical modeling. Geomorphologists work within disciplines such as physical geography, geology, geodesy, engineering geology, archaeology, climatology and geotechnical engineering. This broad base of interests contributes to many research styles and interests within the field.
The enzyme-linked immunosorbent assay (ELISA) is a commonly used analytical biochemistry assay, first described by Engvall and Perlmann in 1971. The assay uses a solid-phase enzyme immunoassay (EIA) to detect the presence of a ligand in a liquid sample using antibodies directed against the protein to be measured. ELISA has been used as a diagnostic tool in medicine, plant pathology, and biotechnology, as well as a quality control check in various industries.
In biology, tissue is a cellular organisational level between cells and a complete organ. A tissue is an ensemble of similar cells and their extracellular matrix from the same origin that together carry out a specific function. Organs are then formed by the functional grouping together of multiple tissues.
Gauss's Theorema Egregium is a major result of differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem is that Gaussian curvature can be determined entirely by measuring angles, distances and their rates on a surface, without reference to the particular manner in which the surface is embedded in the ambient 3-dimensional Euclidean space. In other words, the Gaussian curvature of a surface does not change if one bends the surface without stretching it. Thus the Gaussian curvature is an intrinsic invariant of a surface.
Wood carving is a form of woodworking by means of a cutting tool (knife) in one hand or a chisel by two hands or with one hand on a chisel and one hand on a mallet, resulting in a wooden figure or figurine, or in the sculptural ornamentation of a wooden object. The phrase may also refer to the finished product, from individual sculptures to hand-worked mouldings composing part of a tracery.
Soap films are thin layers of liquid surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Thus, foams are composed of a network of films connected by Plateau borders. Films are used as model systems for minimal surfaces, which are widely used in mathematics.
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.
A washer is a thin plate with a hole that is normally used to distribute the load of a threaded fastener, such as a bolt or nut. Other uses are as a spacer, spring, wear pad, preload indicating device, locking device, and to reduce vibration. Washers often have an outer diameter (OD) about twice their inner diameter (ID), but this can vary quite widely.
A grinding machine, often shortened to grinder, is one of power tools or machine tools used for grinding, it is a type of machining using an abrasive wheel as the cutting tool. Each grain of abrasive on the wheel's surface cuts a small chip from the workpiece via shear deformation.
Moulding, also known as coving(United Kingdom, Australia), is a strip of material with various profiles used to cover transitions between surfaces or for decoration. It is traditionally made from solid milled wood or plaster, but may be of plastic or reformed wood. In classical architecture and sculpture, the molding is often carved in marble or other stones.
A surface plate is a solid, flat plate used as the main horizontal reference plane for precision inspection, marking out (layout), and tooling setup. The surface plate is often used as the baseline for all measurements to a workpiece, therefore one primary surface is finished extremely flat with tolerances below 11.5 μm or 0.0115 mm per 2960 mm for a grade 0 plate. Surface plates are a common tool in the manufacturing industry and are often permanently attached to robotic-type inspection devices such as a coordinate-measuring machine. Plates are typically square or rectangular.
Lapping is a machining process in which two surfaces are rubbed together with an abrasive between them, by hand movement or using a machine.
In soil science, Horton overland flow describes the tendency of water to flow horizontally across land surfaces when rainfall has exceeded infiltration capacity and depression storage capacity. It is named after Robert E. Horton, the engineer who made the first detailed studies of the phenomenon.
Surface runoff is the flow of water that occurs when excess stormwater, meltwater, or other sources flow over the Earth's surface. This can occur when the soil is saturated to full capacity, and rain arrives more quickly than soil can absorb it. Surface runoff often occurs because impervious areas do not allow water to soak into the ground. Surface runoff is a major component of the water cycle. It is the primary agent of soil erosion by water. The land area producing runoff that drains to a common point is called a drainage basin.
A term typically used by Earth scientists, a sabkha is a coastal, supratidal mudflat or sandflat in which evaporite-saline minerals accumulate as the result of semiarid to arid climate. Sabkhas are gradational between land and intertidal zone within restricted coastal plains just above normal high-tide level. Within a sabkha, evaporite-saline minerals sediments typically accumulate below the surface of mudflats or sandflats. Evaporite-saline minerals, tidal-flood, and eolian deposits characterize many sabkhas found along modern coastlines. The accepted type locality for a sabkha is at the southern coast of the Persian Gulf, in the United Arab Emirates. Sabkha is a phonetic translation of the Arabic word used to describe any form of salt flat. A sabkha is also known as a sabkhah,sebkha, or coastal sabkha.
A glass stirring rod, glass rod, stirring rod or stir rod is a piece of laboratory equipment used to mix chemicals. They are usually made of solid glass, about the thickness and slightly longer than a drinking straw, with rounded ends.
In manufacturing and mechanical engineering, flatness is an important geometric condition for workpieces and tools.
A frying pan, frypan, or skillet is a flat-bottomed pan used for frying, searing, and browning foods. It is typically 20 to 30 cm in diameter with relatively low sides that flare outwards, a long handle, and no lid. Larger pans may have a small grab handle opposite the main handle. A pan of similar dimensions, but with less flared vertical sides and often with a lid, is called a sauté pan. While a sauté pan can be used like a frying pan, it is designed for lower-heat cooking methods, namely sautéing.
