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What is geometry in nature?

Updated: 11/4/2022
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GEOMETRY Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. USES : How much concrete is needed for a footing with these dimensions?, or how much Fencing is needed to enclose the region in this sketch. Carpentry generally does not require much formal education, but some of their applicants thought all they had to do was show up. Geometry being used in : (a) Computer graphics is based on geometry - how images are transformed when viewed in various ways. (b) Computer-aided design, computer-aided geometric design. Representing shapes in computers, and using these descriptions to create images, to instruct people or machines to build the shapes, etc. (e.g. the hood of a car, the overlay of parts in a building construction, even parts of computer animation). (c) Robotics. Robotic vision, planning how to grasp a shape with a robot arm, or how to move a large shape without collission. (d) Medical imaging - how to reconstruct the shape of a tumor from CAT scans, and other medical measurements. Lots of new geometry and other math was (and still is being) developed for this. (e) Structural engineering. What shapes are rigid or flexible, how they respond to forces and stresses. Statics (resolution of forces) is essentially geometry. This goes over into all levels of design, form, and function of many things. I have attended some interesting architecture and design conferences where all of this flows together - sometimes (in North American culture) with people knowing too little geometry to do some of the things well. (f) Protein modeling. Much of the function of a protein is determined by its shape and how the pieces move. Mad Cow Disease is caused by the introduction of a 'shape' into the brain (a shape carried by a protein). Many drugs are designed to change the shape or motions of a protein - something that we are just now working to model, even approximately, in computers, using geometry and related areas (combinatorics, topology). (g) Physics, chemistry, Biology, .... . Symmetry is a central concept of many studies in science - and also the central concept of modern studies of geometry. Students struggle in university science if they are not able to detect symmetries of an object (molecule in stereo chemistry, systems of laws in physics, ... ). the study of transfromations and related symmetries has been, since 1870s the defining characteristic of geometric studies.

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