Beyond the Book – Geometry


DO WE STILL NEED TO LEARN GEOMETRY? Many kids wonder why they have to endure hours learning about lengths, areas, volumes and angles. Surely all this ‘old stuff’ can’t still be relevant today?


The truth is, students today might be surprised at how relevant subjects like geometry actually are in our everyday lives.


Let’s take an example every modern student can relate to: Video games.

When you play a video game, do you notice how realistic the graphics are in the background? The digital landscapes in your favourite game was designed with the help of geometry.


Geometry helps computer designers to build virtual realities that resemble real life. Most serious gamers will tell you that speed is far more important than how real the graphics appear. Fortunately, with the help of geometry, you can have both.


Geometric computations allow the programmers to create paths around the obstacles so that the virtual characters can move around in their ‘world.’ Video game engines will use something called ‘raycasting’, which is a technique that simulates a 3-D world using a 2-D map. Using this form of geometry helps speed up processing because calculations are only done for the vertical lines on the screen.


So now that we know geometry is used in video games, what other applications does it have? Well, before we get into the many practical uses of one of our favourite subjects, let’s take a short look into the history of geometry.


THE HISTORY OF GEOMETRY


There once was an ancient Greek mathematician in Alexandria, Egypt named Euclid. Euclid completely changed the math game during his lifetime. He acquired the nickname “Father of Geometry” because of his ground-breaking work in math, especially his most well-known collection of works, called Elements which outlines some of the most fundamental principles of geometry. The most basic form of geometry is still called Euclidean geometry.


The word “Geometry” is derived from the Greek word “Geo” and “Metron” which translates to Earth and Measurement. “Earth’s Measurement, “as the name describes, deals with the characteristics of figures as well as shapes. Geometry shows us how to determine areas, volumes, and lengths which is what our world is made up of.


Later, when the Pythagoreans came along, they introduced numbers into geometry in the form of numerical values of lengths and areas. Nowadays, modern geometry has strong ties with physics, and is a crucial part of new physical concepts such as relativity and string theories.


HOW DO WE USE GEOMETRY IN OUR EVERYDAY LIVES?



Now that we know how geometry came to be, let’s look at some more ways it’s used every single day.

Technology - In our fast-paced world, that seems to be governed by technology, this is where we can find the most common examples of geometry in everyday life. Computer programmers are able to make all these systems work because geometry is applied to all the underlying concepts. Be it in general computing, the video games we spoke about earlier or even advanced robotics, geometry helps characters move, landscapes be constructed and even helps robots to ‘see’. Basically, everything we love about the digital world is only possible because of geometry.


Mother Nature – On the opposite side of the spectrum from technology, is the natural world we live in. You might find it surprising, but geometry is also present and no less important here. If you look closely at all the trees, flowers and leaves around you, you will notice all the beautiful and intricate different geometrical shapes and patterns that are visible on them. Every leaf is a different size, shape and symmetry. The details and intricacies of each part of nature allows us to further study and understand the world we live in.


Building – When we think of geometry, the most common application many people think of is usually architecture. Before any architectural form can be constructed, math and geometry are used to take the structural blueprint of the building from an idea, into a reality. The theories of proportions and symmetries are not only used to make buildings visually appealing but to ensure that they are stable and safe in the face of risk factors like high force winds. Think of that next time you are sitting inside while a storm rages on outside. Geometry is keeping you safe.


Households – Could you imagine that geometry is hiding in every corner of our homes? Do you like eating delicious food? Geometry is an important part of the cooking and baking process. Ingredients need to be used in accurate proportions and ratios if a dish is to be just right. Even our doors, windows, beds, chairs, etc are displaying geometrical concepts in their different shapes. Do you notice different geometric patterns on the carpets or rugs? Interior designers will make use of geometry to ensure a space is used in a way that makes it visually appealing. They will also use vases, paintings, and various decorative pieces, made from different geometric shapes and have different patterns made on them to make a home look beautiful.


Art - Art is defined as “the expression or application of human creative skill and imagination, typically in a visual form such as painting or sculpture, producing works to be appreciated primarily for their beauty or emotional power.” It can also be defined as “the formation of shapes and figures, a straightforward understanding of 2D & 3D, familiarity about spatial concepts, and an assessment of patterns & measurement.” Using this second definition, it’s clear to see how geometry is an integral part of art. When an artist makes use of a circle, triangle, square, mandala, or octagon, they are making use of geometrical forms. Some artists even use these geometrical elements as a way to create the illusion of the third dimension. This art is known as Optical or ‘Op Art.’


Sports – Could you imagine that even your favourite sport would make use of geometry? It’s true! Not just in the buildings we gather in to watch sporting events but the shapes of the fields or pitches themselves. The athletic field uses geometry to help predict the movement of the players and enhance their performances. Look at the rectangular shape of a hockey, soccer, basketball or football field. These shapes are very intentional. The positions of the players are also mapped out using geometry. For example, the corner kick spots, goal posts, arcs, D-section, and centre circle are marked on the field. Angles are also used on track fields because many of them are semi-circular. Everywhere you look in sports, geometry is being used in some way.


Medical – We trust in our doctors to help us feel better. Our doctors, trust in the principles of geometry to be able to do their jobs effectively. How? Well, they make use of X-rays, ultrasounds, MRIs, and nuclear imaging to determine what is wrong when we come to them with a problem. All medical equipment like this, requires the reconstruction of shapes. They look at the shapes of organs, bones, and tumours to determine a problem. What is the reconstruction of shapes based on? You guessed it - geometry.


GEOMETRY IS EVERYWHERE


As you can see, geometry affects us even in the most basic details of our lives. No matter what the form, it helps us understand how the world works and how we fit into it. Geometry also helps us live a better quality of life by allowing us to excel at our jobs, beautify the spaces we live and enhance our performances in them.


Next time you find yourself wondering if geometry is relevant today, think about the video game you are about to play or the delicious meal waiting for you. Think about the sports game you want to watch this weekend, the flowers your mum loves or the comfortable bed you’re going to sleep in.


If you look around you, the magic of geometry is everywhere and if you don’t see it, you aren’t looking hard enough.


If you’re anything like us, that has left you feeling hugely inspired! No matter what further study or career you’re considering, a solid base in math will be a huge asset. Contact us today to book a session with one of our expert math tutors.


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