Math feels good when we get that A-HA feeling. But sometimes, the “Eureka” moment strikes unexpectedly. Natural shapes are all around us. The study of geometry has changed rather dramatically in the last few decades.
As static classroom textbooks evolved into dynamic, engaging, and personalized journeys, students’ interest in the subject has also evolved. Thanks to the field of mathematics, we don’t need a pencil and a ruler to be able to tell what these shapes are anymore—or what they might look like if they stretched on forever.
Interactive tools: the power to see math anew
In essence, geometry is not about trying to memorize formulas. Rather, it’s about understanding the patterns and structures which describe our physical world. The truth is that we’re often doing geometric reasoning without even knowing it. If you’ve ever equally sliced a hot pizza or backed up a car into a parallel parking spot, you were doing geometry (even if you didn’t know).
Traditional geometry lessons usually involve static images, rulers, and compasses. For students who may be exploring geometry for the first time, there exist more engaging ways to start the conversation about geometry than charts and graphs. For instance, the arcs of a skateboard ramp or the mosaic pattern in a tiled floor can suddenly crystallize those complex classroom concepts.
Digital Geometry Applications
If you’ve had the joy of learning geometry with technology, you already know the power of visualization. With apps for smartphones and tablets, geometry becomes tangible. Just imagine pulling those vertices of a triangle as if on a smartphone screen. As you pull, watch the angles and side lengths change in real time.
Virtual and Augmented Reality
The field of teaching is being revolutionized by virtual reality (VR) and augmented reality (AR), and the subject of geometry is no exception. Oculus VR’s Shapespark and Merge Cube apps allow students to interact with 3D objects in immersive ways. Imagine holding a virtual pyramid, walking around it, and playing your way through the faces to see how they connect.
Coding and Geometry
Geometry reveals patterns, and that’s most of what computer code is. Other interesting avenues include coding platforms such as Scratch and Python. Video games, music concert visualizers, and other coding-related applications can pave the way to studying computer science in the future. When proceeding on to studying computer science, students will begin to learn not only geometry, but also logic and problem-solving skills.
Math and programming are two sides of the same coin. Writing programs that turn code into shapes and animations can spark curiosity and light a life-long flame. Because geometry is so closely related to fractals, you can actually see geometry as something symmetrical, balanced, and (yes) beautiful.
Real-World Applications: From Architecture and Arts to Placemaking and Sports
As you could tell from the examples earlier, geometry can feel extremely abstract and disconnected from the real world—that is, until the real-world examples are thrown into the mix. Suddenly, classic geometry becomes interactive as it bridges the gap between abstract concepts and practical applications across multiple fields, such as:
Architecture and Design
Lines, angles, curvatures, and pivot points all play crucial roles in architecture and design. Geometry is used by architects to make stable, pleasingly beautiful structures. Interactive “Computer-Aided Design” software (also known as CAD) is used by designers to try out shapes and dimensions before the construction even gets underway. By harnessing principles of geometry, architects and designers can innovate functional spaces with timeless looks.
Sports Analytics
Geometry matters a great deal in all types of sports strategies—from finding the perfect basketball shot arc to projecting optimal soccer kick trajectories. Athletes can use geometry to study their strategy and improve their performance. In the realm of calling fouls and deciding whether one millimeter over the line counts as a goal, geometry is indispensable for sports analytics.
Art and Animation
At its core, all art and animation require geometry to bring imagination to life. Artistic creation is based on geometric principles. Geometric algorithms are used by Pixar animators to render lifelike characters, and interactive tools are used by graphic designers to make stunning visual works. Vivid detail wouldn’t be so vivid if it weren’t mathematically captivating to our eye.
Environmental Planning
Geometry is essential to placemaking as well. Urban design problems can be solved by leveraging geometric principles: designing efficient road networks, planning sustainable public spaces, and more. Through analyzing maps and schematics, planners can build livable and more sustainable spaces that cater to all who inhabit them.
Once kids graduate high school and go off into the real world, geometry will be all around them – and you won’t be there to tell them what it means. How well they prepare in school today, will influence the way they see the world, how willingly they accept information thrown at them and how much they’re able to utilize their logic to spot trends, both good and bad, in their day-to-day life.
How Geometry Encourages Critical Thinking
Most parents have no idea their kids are doing geometry when they’re playing Roblox. While physical education remains the supreme way to discover the world, video games like Tetris – in the right amounts – can be educational. Interactive geometry has been shown to turn students from passive learners to active problem solvers. Teachers can now use a touch screen to pose thought provoking questions like:
- If you change the shape of a triangle, what happens to the triangle’s angles?
- Could you design a “fractal” tessellation that fills out a whole plane without any gaps?
These sorts of questions invite experimentation, prediction, and real-time learning from mistakes to further the child’s understanding of how the world works. There’s no better way to cultivate a lifelong love of discovery and curiosity than to become familiar with how shapes work from a young age.
Accessibility and Inclusion
Geometry can be something you not only see or hear, but actually touch. A number of interactive geometry platforms are free and available on many different devices, democratizing high-quality mathematical education. Different learning styles are catered for: visual learners are helped by dynamic diagrams, kinesthetic learners are engaged by shape manipulation. This inclusive approach to classroom instruction allows all to have the chance to get up close and personal with geometry and to feel it for themselves.
Interactive Geometry: The Future
First came the abacus, then the chalkboards, and now the iPads and VR headsets. The possibilities are endless with technology. Personalized learning algorithms are themselves being developed by machine learning and AI. The future of geometry is interactive, immersive, and full of potential new ways to learn.
Geometric exploration will continue to expand more deeply into virtual and augmented reality, so students can step into mathematical environments. As technology advances, so will the integration of lesson planning alongside that technology, which is already starting to revolutionize education.
A Call to Explore
Geometry is not just a subject; it is a way of seeing the world. Learning geometry has become more interactive, easier to learn, and directly applicable to life. The world of interactive geometry has exciting potential whether you are a student, educator, or parent.
Math doesn’t have to be hard. If you’re struggling with geometry, get ready to change your entire stance on math. There’s no better time to get your hands on the beautiful world of shapes that is out there every day, helping students to fall in love with studying. At OMC, we help students to fall in love with geometry, and more. Contact us today to try a free lesson.
