Geometry is a popular branch of mathematics that is often studied in college. This field of math explains the specific relationship between size and shape, while also explaining the nature of numbers. First appearing in the ancient world as formulas used for construction and solving problems, geometry has evolved. Dating back to 3000 B.C., this mathematical branch has played a major role in many cultures and was first used when constructing of pyramids, using a square and four triangular sections.
To study geometry successfully in school, one must have an understating of the history and various uses of this form of math. Taught in advanced education courses, modern geometry can be difficult to learn and some students will need online geometry help, but it was not possible to get help earlier, so let’s get acquainted with the history of geometry. Here, we take a look at how geometry has evolved and how some great advancements have made this field of mathematics one of the most significant to date.
Greek Contributions and Euclidean Geometry
Through years of research, we have learned that Greek mathematicians are the fathers of geometry. There are two main mathematicians that are associated with the evolution. This type of math is taught in high school and provided the basis for other types of geometry.
Pythagoras
Known as the first to create basic geometric concepts, Pythagoras came up with a group of people that included students and followed. Together, they discovered the Pythagorean Theorem. This states that the sum of the square of right angle triangle legs are equal to the square of the hypotenuse. It was later added that the sum of all interior angles of any triangle will always be 180 degrees.
Euclid
As a student, you will research the beginning of geometry and will find that Euclid played a key role in advancements. A text titled Elements was written in 300 BC. In this, Euclid introduced Euclidean Geometry. With this, propositions would be able to be proven by using sets of statements accepted as truth.
Major postulates were listed in this text, and many allowed Euclid to create a piece of planar geometry. These included:
- Straight line segments could be created by joining any two points
- Extend finite straight line continuously
- Circles can be drawn using the straight line segments with one point being the center and one segment as radius
- Right angles are equal
One key postulate from the text is the parallel postulate. This states, “Of the lines are drawn which intersect a third line in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended infinitely.” For almost 2000 years following Elements, mathematicians tried to provide the fifth postulate as a theorem.
Non-Euclidean Geometries
This type of geometry came from an attempt to fix the fifth axion. It is an extension of Euclid’s findings that is applied to three dimensional objects. This branch was developed by Carl Friedrich Gauss. Also referred to as hyperbolic geometry, this type of math will usually include spheres and ellipses. Students will be faced with solving complex geometry problems. If you need help with geometry, you can work with professional tutors that can walk you through the process to come up with the right geometry solution to complete your assignments.
If you are studying math on an academic level, you will find that this branch is useful in showing that certain theorems are different when applied to three dimensions. Non-Euclidean geometry classes in college are considered modern geometry and can be a struggle for some students, which is why help is available! This branch has begun to play an important role in science and technology. Even if you are not pursuing a degree in mathematics, these courses can be beneficial.
Those that are following a science or technology career will benefit from adding some non-Euclidean classes to your course load. This branch is used in many ways in today’s technology, especially with an increased use of GPS systems and devices. Even those pursuing a career in graphic arts will make use of this since they are always working with 3D graphics and animations.
Recent Developments
The most recent advancement in this branch is based on fractals. Developed by Benoit Mandelbrot, an IBM researchers, it defines shapes using specific rules. A fractal is a pattern with no definite ending, created by repeating a simple process. It can also be used to understand complex systems, not just shapes. For example, variations in human heartbeats or the timing of an earthquake are both cases where fractal geometry can be used to describe what otherwise would be unpredicted. It has also been used in stock markets to describe market activity regarding profits or losses made by traders.
Today, fractal math has multiple practical uses, from producing realistic computer graphics, file compression systems in computers, and even diagnosing certain disease.
Conclusion
There are many pros to studying geometry and for thousands of years, this type of math has been used worldwide and in many ways. It remains an important mathematical branch today. Studying math continues to stand the test of time and there are many applications. From designing buildings to navigating aircraft, this field plays a role in everyday life.