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Euclidean Geometry - Entertaining Geometry

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Geometry was invented by Euclid from the Plato Academy in 325-265 b.c. The way geometry got its name, is from the ancient greek words geo – meaning earth, and metron meaning measurement. He wrote geometry in a treatise which consisted of thirteen books. Each book represented a chapter. These books were titled The Elements of Geometry. They were known then as the ideal axiomatic form of Geometry whereas now they are known as Euclidean Geometry. Though Euclid did have some help from Pythagoras of Samos. Pythorgoras was the other contributor to creating geometry. Pythagoras was an ancient greek ionian philosopher. He was the eponymous founder of Pythagoreanism. He also contributed to many other things including The Five Regular Solids, theory of proportions, and the sphericity of the earth.However Euclid and Pythorgoras weren’t the only people to have discovered Geometry and use it to their advantage. Back in ancient Egypt, scientists have found proof that the Egyptians had also used Geometry in several different ways. Those ways including surveying land, constructing pyramids, and astronomy. With such knowledge, the Egyptians were able to build the pyramids the way they are now. Along with the Egyptians came the indians and chinease. The next great advancement in geometry happened during the 17th century. This was when Rene Descartes discovered coordinate geometry. This new kind of geometry opened up the doors to calculus and physics, along with new proofs.There are many different individuals that made major contributions to geometry. Few of those being Mozi from China, Brahmagupta from India, Archimedes of Sicily, and Thales of Miletus. With Mozi’s early knowledge of Geometry his followers made the Mo Jing. They compiled this after his death and it was possibly the earliest book with such knowledge to survive the burning books order that the current dynasty in rule had ordered. Later on with the help of Mo Jing the nine chapters of mathematical arts was made. In classical Indian Geometry, Brahmagupta made a large contribution with his astronomical work Brahma Sphuta Siddhanta. The book contained the ‘basic operations’ including cube roots, fractions, ratio and proportion, and barter. It also had ‘practical mathematics’ which consisted of mixture, mathematical series, plane figures, stacking bricks, and piling grain. With all this the Brahmagupta theorem was created.

Archimedes of Sicily is often referred to as one of the greatest Greek mathematicians, and for a good reason too. Archimedes is known for the discovery of the relations between the surface and volume of a sphere and its cylinder. He’s also known for Archimedes’ principle and Archimedes’ screw. Finally we have one of the Seven Sages of Greece. Thales of Miletus is the first philosopher in western tradition. The Seven Sages of Greece were a group of early 7th and 6th century philosophers. Thales was famous for his beliefs. One of his beliefs that he’s most famous for is cosmological doctrine that states that water is the principle of all things. Later on though, Thales begins to claim that water is the origin of all things. It’s most likely that he came to this conclusion from observing water turning into air, slime, and earth.

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Geometry can be used in many real world scenarios such as construction blueprints, nanotechnology, computer graphics, visual graphs, video game programming, and virtual reality creation. Geometry is also used in global positioning systems, astronomy, and cartography.In computer graphics geometry is used for mapping out. The way the creators of the games have mapped everything out digitally in the game is a form of using geometry. They have to plot points around the entire ‘map’ for the players to go to or come from. They plot the points geometrically using different computer softwares and other forms of math. It’s the same way with the vr and other game softwares. They focus on making things look as realistic and nice as possible to make the gameplay enjoyable for players. At the same time they do this they make sure that everything goes accordingly in the program. In the actual real world geometry is used to map out buildings and structures correctly and mathematically so that they do not collapse. They do this by mapping out blueprints. Take Architects for instance. They use geometry in designing the buildings they make. One way architects use geometry is in angle measurements. The architect needs to know the degree and measurement of an angle to be able to build what they need. Take this example, if you’re building a table that’s a rectangle like shape, then you need to know the angle measurements of it to be able to build it. Another way architects use geometry is by using certain shapes for certain buildings. Architects need to know the perimeter of the area that they are working/building in to be able to determine the shapes of the structure that they are building. The last way that I learned architects use geometry for is by using the Pythagorean Theorem.The Pythagorean Theorem is used in architecture is through design and measurements of a monument or structure. They also use the theorem to calculate the heights of the building and the length of the walls.

Other ways geometry is used in the real world is through biology, medicine, and physical science. In the medical area geometry is used in dental hygiene and radiology. In dental hygiene it’s used by people called Dental Hygienist’s. A dental hygienist is someone that cleans teeth, examines the patient for any oral disease, and in some cases apply fluoride treatments to the patients. Now it doesn’t seem like geometry would play part in anything remotely close to dental studies, but it does. For a dental hygienist to do their job correctly they need to look at the shapes and dimensions of a patient’s teeth, count/name the teeth, and also identify the planes on the teeth.

The other way geometry can be used in the medical field is in Radiology. A radiologist uses technology such as x-rays, ultrasounds, MRI’s, nuclear imaging, and many other things. Geometry skills can be applied when reconstructing organs, bones, and any other item of the human body.The way it’s applied is when they measure the bones and other parts of the human body with film. The body parts should be parallel and the beam should be perpendicular to the part and the film. There are certain techniques used in geometry that apply to this. These techniques are paralleling techniques and bisecting angle techniques.

The last way Geometry can be used in real life is in Biology. Much like architecture biology uses geometry to map out the helical structures found in the membrane structure in the cells of the body.These are nicknamed ‘Terasaki ramps’ after the person that discovered them. They were found in an organelle called the endoplasmic reticulum. Now, a trio of scientists describe ER geometry using the language of theoretical physics. “Our work hypothesizes how the particular shape of this organelle forms, based on the interactions between Terasaki ramps,” said Huber, who is a deputy director of UCSB’s Kavli Institute for Theoretical Physics. This theoretical work provides a deeper story for the shapes found in cell interiors.

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