HISTORY OF GEOMETRY

Euclid's The Elements of Geometry (c.300 BCE), was one of the most important early texts on geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as Euclidean geometry.

In the early 17th century, there were two important developments in geometry. The first and most important was the creation of analytic geometry, or geometry with coordinates and equations, by Rene Descartes (1596–1650) and Pierre de Fermat (1601–1665). The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry is the study of geometry without measurement, just the study of how points align with each other.

Geometry is still feeling the effects of two developments from the nineteenth century. Two of the master geometers of the time were Bernhard Riemann, working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems.

As a consequence of these major changes in the conception of geometry, the concept of 'space' became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics. The traditional type of geometry was recognised as that of homogeneous spaces, those spaces which have a sufficient supply of symmetry, so that from point to point they look just the same

Contemporary geometry

Some of the representative leading figures in modern geometry are Michael Atiyah, Mikhail Gromov, and William Thurston. Geometry now is, in large part, the study of structures on manifolds, that have a geometric meaning in the sense of the principle of covariance that lies at the root of general relativity theory, in theoretical physics.

Contemporary Euclidean geometry

The study of traditional Euclidean geometry is by no means dead. It is now typically presented as the geometry of Euclidean spaces of any dimension, and of the Euclidean group of rigid motions. The fundamental formulae of geometry, such as the Pythagorean theorem, can be presented in this way for a general inner product space.

Euclidean geometry has become closely connected with computational geometry, computer graphics, discrete geometry, and some areas of combinatorics. Momentum was given to further work on Euclidean geometry and the Euclidean groups by crystallography and the work of H. Geometric group theory is an expanding area of the theory of more general discrete groups, drawing on geometric models and algebraic techniques.

Algebraic geometry

The field of algebraic geometry is the modern incarnation of the Cartesian geometry of co-ordinates.

The geometric style which was traditionally called the Italian school is now known as birational geometry. Objects from algebraic

geometry are now commonly applied in string theory, as well as diophantine geometry.

Methods of algebraic geometry rely heavily on sheaf theory and other parts of homological algebra. For practical applications, Gröbner basis theory and real algebraic geometry are major subfields.

Differential geometry

Differential geometry, which in simple terms is the geometry of curvature, has been of increasing importance to mathematical physics since the suggestion that space is not flat space. Contemporary differential geometry is intrinsic, meaning that space is a manifold and structure is given by a Riemannian metric, or analogue, locally determining a geometry that is variable from point to point.

Topology and geometry

The field of topology, which saw massive development in the twentieth century, is in a technical sense a type of transformation geometry, in which transformations are homeomorphisms. Contemporary geometric topology and differential topology, and particular subfields such as Morse theory, would be counted by most mathematicians as part of geometry.

Arts & Crafts

Arts and crafts comprise a whole host of activities and hobbies that are related to making things with one's hands and skill. These can be sub-divided into handicrafts or "traditional crafts" (doing things the old way) and "the rest". Some crafts have been practised for centuries, while others are modern inventions, or popularisations of crafts which were originally practised in a very small geographic area.

Most crafts require a combination of skill, speed, and patience, but they can also be learnt on a more basic level by virtually anyone. Many community centres and schools run evening or day classes and workshops offering to teach basic craft skills in a short period of time. Many of these crafts become extremely popular for brief periods of time (a few months, or a few years), spreading rapidly among the crafting population as everyone emulates the first examples, then their popularity wanes until a later resurgence.

Arts and crafts also refers to the Arts and Crafts movement, a late 19th century design reform and social movement. Its proponents were motivated by the ideals of William Morris and John Ruskin, who proposed that in pre-industrial societies, such as the European Middle Ages, people had achieved fulfillment through the creative process of handicrafts. This was held up in contrast to what was perceived to be the alienating effects of industrial labour.

All this is the work of thousands of unsung, unappreciated artisans and crafts persons who make magic with their very hands. They are the ones who make those fabulous tie-and-dye skirts, those

fantastically embroidered Gujarati cholis, that lacquered furniture and that beautifully studded silver jewellery. India may be a land of farmers but it is equally a land of artisans.

Unfortunately, Indian arts and crafts have been teetering on the edge of extinction for a long time. Demand for indigenous arts and crafts nose-dived with the setting up of large-scale industry in India. After all, in a poor country like India, machine-made saris – to give you but one example – are cheaper and therefore more affordable than handloom saris. The list is endless. This has left artisans with little choice but to abandon their age-old professions and become common laborers, factory workers or government clerks. In either case, the loss has been of ours.

Thankfully, efforts have been made by both government and non-government agencies to keep our art and craft tradition alive and kicking. Here then is an overview of the major arts and crafts of India.

These activities are called crafts because originally many of them were professions under the guild system. Adolescents were apprenticed to a master-craftsman, and they refined their skills over a period of years in exchange for low wages. By the time their training was complete, they were well-equipped to set up in trade for themselves, earning their living with the skill that could be traded directly within the community, often for goods and services. The Industrial Revolution and the increasing mechanisation of production processes gradually reduced or eliminated many of the roles professional craftspeople played, and today "crafts" are most commonly seen as a form of hobby or art.

The term craft also refers to the products of artistic production or creation that require a high degree of tacit knowledge, are highly technical, require specialized equipment and/or facilities to produce,

involve manual labour or a blue-collar work ethic, are accessible to the general public and are constructed from materials with histories that exceed the boundaries of western art history, such as ceramics, glass, textiles, metal and wood. These products are produced within a specific community of practice and while they differ from the products produced within the communities of art and design, the boundaries of such often overlap resulting in hybrid objects. Additionally, as the interpretation and validation of art is frequently a matter of context, an audience may perceive crafted objects as art objects when these objects are viewed within an art context, such as in a museum or in a position of prominence in one's home.

Types of arts and crafts

There are almost as many variations on the theme of "arts and crafts" as there are crafters with time on their hands, but they can be broken down into a number of categories:

Banner-making Calligraphy

Canvas work

Cross-stitch

Crocheting

Curve stitching

Embroidery

Felting

Knitting

Lace-making

Lucet

Macrame

Millinery

Needlepoint

Patchwork

Quilting

Ribbon embroidery

Rug making

Sewing

Shoemaking

Spinning (textiles)

Spirelli (also see Scrapbooking)

String art

Tapestry

Tatting

T-shirt art

Weaving

Crafts involving wood, metal or clay

Cabinet making Carpentry

Chip carving

Jewelry

Marquetry

Metalworking

Pottery

Sculpture

Wood burning

Wood turning

Woodworking

Fretwork

Founders of the Arts and Crafts movement

Textile

Banner-making · Canvas work · Cross-stitch · Crocheting · Curve stitching · Embroidery · Felting · Friendship bracelet · Knitting · Lace-making · Lucet · Macrame · Millinery · Needlepoint · needlework · Patchwork · Quilting · Ribbon embroidery · Rug hooking · Rug making · Sewing · Shoemaking · Spinning (textiles) · String art · Tapestry · Tatting · Tie-dye · Weaving

Paper

Bookbinding · Calligraphy · Cardmaking · Card Modelling · Collage · Decoupage · Embossing · Iris folding · Marbling · Origami · Papercraft · Papier-mâché · Scrapbooking · Stamping

WoodCabinet making · Carpentry · Chip carving · Intarsia · Marquetry · Wood burning · Wood carving · Woodturning · Woodworking

CeramicAzulejo · Cameo glass · Ceramics · Glassware · Pottery · Stained glass

Metal Metalworking · Jewellery

Other

Assemblage · Beadwork · Bone carving · Doll making · Dollhouse · Egg decorating · Engraved gems  · Hardstone carving  · Jewellery  · Lathart · Lapidary · Miniatures · Micromosaic  · Mosaic · Pietra dura  · Pressed flower craft · Scrimshaw · Straw marquetry  · Textile arts

DesignDesign is the planning that lays the basis for the making of every object or system. It can be used both as a noun and as a verb and, in a broader way, it means applied arts and engineering (See design disciplines below). As a verb, "to design" refers to the process of originating and developing a plan for a product, structure, system, or component with intention[1]. As a noun, "a design" is used for either the final (solution) plan (e.g. proposal, drawing, model, description) or the result of implementing that plan in the form of the final product of a design process[2]. This classification aside, in its broadest sense no other limitations exist and the final product can be anything from

clothing to graphical user interfaces to skyscrapers. Even virtual concepts such as corporate identity and cultural traditions such as celebration of certain holidays[3] are sometimes designed. More recently, processes (in general) have also been treated as products of design, giving new meaning to the term process design.

The person designing is called a designer, which is also a term used for people who work professionally in one of the various design areas, usually also specifying which area is being dealt with (such as a fashion designer, concept designer or web designer). Designing often requires a designer to consider the aesthetic, functional, and many other aspects of an object or a process, which usually requires considerable research, thought, modeling, interactive adjustment, and re-design. With such a broad definition, there is no universal language or unifying institution for designers of all disciplines. This allows for many differing philosophies and approaches toward the subject. However, serious study of design demands increased focus on the design process

Defining a design process

According to video game developer Dino Dini, in a talk given at the 2005 Game Design and Technology Workshop held by Liverpool JM University, design underpins every form of creation from objects such as chairs to the way we plan and execute our lives. For this reason it is useful to seek out some common structure that can be applied to any kind of design, whether this be for video games, consumer products or one's own personal life.

For such an important concept, the question "What is Design?" appears to yield answers with limited usefulness. Dino Dini states that the design process can be defined as "The management of constraints". He identifies two kinds of constraint, negotiable and non-negotiable. The first step in the design process is the identification, classification and selection of constraints. The process of design then proceeds from here by manipulating design variables so as to satisfy the non-negotiable constraints and optimizing those which are negotiable. It is possible for a set of non-negotiable

constraints to be in conflict resulting in a design with no solution; in this case the non-negotiable constraints must be revised. For example, take the design of a chair. A chair must support a certain weight to be useful, and this is a non-negotiable constraint. The cost of producing the chair might be another. The choice of materials and the aesthetic qualities of the chair might be negotiable.

Dino Dini theorizes that poor designs occur as a result of mismanaged constraints, something he claims can be seen in the way the video game industry makes "Must be Fun" a negotiable constraint where he believes it should be non-negotiable.

It should be noted that "the management of constraints" may not include the whole of what is involved in "constraint management" as defined in the context of a broader Theory of Constraints, depending on the scope of a design or a designer's position.