This blog completely deals with the framework of usage of Augmented Reality in geometry based learning. This provides students do Mathematics and Geometry with ease

Author-V.Rajkumar

Augmented reality is a technology that place or lay a computer generated image on a users view of the real world, thus it will provides a different parts of the images view in a very spatial way. It gives a live of physical world and also it has much space, even one can feel or notice as an involving aspects of real environment. Augment means additive and Reality means situation that actually exists. It adds to the real environment and it is augmented by computer

The first AR comes from the beginning of 20th century "LYMAN FRANK BAUM" published “THE WONDERFUL WIZARD OF OZ” and explained in a clear way and imagined a kind of augmented reality .He describes a "CHARACTER MAKER"-a set of electronic spectacles, that when you view something through them, the spectacles would show a letter on that Person’s forehead regarding their character. The protagonist even jokes that this technology is "a century ahead of the times". AR made its debut in 1968 the scientist IVAN SUTHERLAND developed the AR Head-Mounted Display (HMD) system called “THE SWORD OF DAMOCLES”. By using computer generated graphics, a user can see the simple drawings and it was used for the first time in 1990.It was used by the being researcher” TOM CAUDELL” and later on it became very popular and many techniques have been emerged in this technical world

BENEFITS OF AR IN 3-D GEOMETRY  Augmented reality in education will soon affect the conventional learning process.  AR has the potential to change location and timing of studying, to introduce new and additional ways and methods.  AR in 3-D geometry provides a natural setting for face to face collaboration of teachers and students.  The main advantage of using AR is that students actually see 3-D objects which they until now had to calculate and construct with traditional methods.  We can speculate that by working directly in 3-D space, complex spatial problems and spatial relationships can be comprehended better and faster than with traditional methods.  AR can change the view and capability of thought process humans can have  This solely is enough for better view of the design patter in various fields

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension. Three-dimensional space is a geometric 3-parameters model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labelled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane. In physics and mathematics, a sequence of n numbers can be understood as a location in ndimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. It is commonly represented by the symbol \scriptstyle{\mathbb{R}}^3. This space is only one example of a great variety of spaces in three dimensions called 3-manifolds.

The ordinary way of creating 3D models (a.k.a. 3D modelling) requires people to sit in front of the computer for a long time working with professional software. The license fee of these software are expensive, and it is very time consuming and not easy to learn. Teachers sometimes find difficult to teach students the concept of 3D modelling because the newbie’s need to spend a lot of time to familiarize with the tool interface beforehand. In this paper, we introduce a mobile application that assists students to learn 3D modelling skills and concepts. We provide a natural modelling style with the aid of Augmented Reality (AR). Through a Smartphone user interface, the user builds a model with primitive blocks in a "bottom-up" manner like "LEGO" bricks. These blocks are visualized on the printed marker cards that allow users to manipulate (rotate, translate, etc.) them in the same way of manipulating real building blocks. User studies have been conducted and we have identified some aspects that help people to model 3D objects. AR is used in different purposes. We can easily solve problems in geometry by using AR. Geometry has been one of the most difficult topics in mathematics. Students still have many problems in learning geometry. Our setup uses a stereoscopic head mounted display (HMD) and the personal interaction panel (PIP)-a two handed 3D interaction tool that simplifies 3D model interaction. By using these tools students can be able to solve problems and can easily understand the concept of geometry. To fill the gap of next-generation virtual reality interfaces for mathematics and geometry education we are developing a three dimensional geometric construction tool called Construct3D that can be used in high school and university education. Our system uses Augmented Reality (AR) [Azuma 1997] to provide a natural setting for face-to-face collaboration of teachers and students. The main advantage of using AR is that students actually see three dimensional objects which they until now had to calculate and construct with traditional (mostly pen and paper) methods. We speculate that by working directly in 3D space, complex spatial problems and spatial relationships can be comprehended better and faster than with traditional methods. Augmented Reality toolkit is used in 3-D geometry system, the system utilizes a AR toolkit for tracking and user interaction. It is open source software that uses single ordinary web camera to track planar, Quadratic Markers usually produced on an ordinary office laser printer. This system provides users with basic functions such as constructing common 3-D objects, customising attributes. It is a useful tool for students to improve their study performance, a pedagogical device for lecturers to produce more intriguing and easily comprehensible lectures.