How many times have you heard your kids grumble as they do their math homework? “When will I ever use this?” is a frequent refrain we hear at A Grade Ahead as well. We know that math, especially geometry, has many practical and amazing applications. So, our response is “every day!” Because it often functions in the background, we take the magic of geometry for granted. This blog post highlights just a few ways in which geometry “shapes” our lives.
Recognizing and Measuring Shapes: Day-to-Day Geometry
Geometry studies the properties and relationships between points, lines, angles, curves, surfaces, and solid objects. We recognize shapes in the world around us, for example, when we are driving. Stop signs are usually octagonal, while danger signs tend to be triangular. So, A Grade Ahead starts teaching our pre-kindergarten students about shapes. More information about our pre-kindergarten curriculum is available here.
We measure two- and three-dimensional shapes every day as well. Say you are remodeling a room and want to change out the carpet. To know how much to budget for the new flooring, you have to know how much flooring you need. For that, you need to calculate the area of the floor. When you fill your pool, though, you measure its volume to determine how much water you will use. Lastly, how do you know how much wrapping paper to use? You calculate the surface area of the box! A Grade Ahead’s math curriculum frequently poses these real-life questions to students.
Representing the World Around Use: Geometry in Art
Although sometimes we think of art and math as separate and unrelated, artists rely on geometry too! Most artists use lines, angles, and shapes to bring their creations to life in two-dimensional or three-dimensional formats. But some artists specialize in geometric art, which features geometric shapes and lines to represent ideas. Other artists use geometry to show proportion, perspective, and symmetry.
Perspective, for example, allows artists to depict three-dimensional objects, including people, in two dimensions. This technique is based on the concept that objects seem to get smaller the farther they are away from the viewer. In geometry, we show this using dilation and vectors. First, establish a vanishing point, which is the point where the lines of the object come together, and the object “vanishes.” Then, draw the outline of the image. Once you have the image sketched out, use dilation to either shrink it or make it bigger. Lastly, you connect the two outlines with lines or vectors. A Grade Ahead teaches this concept in our upper-level geometry curriculum. For more information, check out our program here.
Building the Man-Made Environment: Arcs and Trigonometry
Builders and architects have been using geometry from almost the very beginning. Not only do they need to calculate proportion in their designs, but they also need to measure angles and curves. The domes and arches that seem magical to us today, for example, were built by measuring the arcs. An arc is a section of a circle or an ellipse, and an arch or a dome is a semicircle. This means that soaring arches and domes we marvel at are only possible if the arcs have been measured just so.
Architects also use trigonometry, though. Trigonometry measures a triangle’s angles and side-lengths. For example, some roofs need to be pitched at right angles to be aesthetically pleasing but also to keep water and snow from collecting on the roof. To do that, builders use trigonometry to determine the exact angles at which the bottom edge of the building’s roof must meet the top edge of the walls.
The structural and civil engineers who make our buildings and bridges stand up also use trigonometry. They use it to calculate the forces that will have an impact on the “skeletons” of these structures. For example, girders or beams bear the weight of the walls, floors, and roofs of buildings. Structural engineers use trigonometry to calculate the force that weight will have on the beams and therefore how strong the beams need to be. To do this, they sometimes break down the vertical and horizontal components of the force on these structures into right triangles and use trigonometry to calculate the angles. They also use parabolic formulas to determine how far the beams can bend without breaking. A Grade Ahead teaches these concepts and more in our Algebra I, Geometry, and High School Math curricula.
Utilizing Computer Science and Technology: Geometry in the Background
These wonders of geometry are always at work, even if we do not do the calculations ourselves. The next time you take a selfie, consider the ways in which your phone uses geometric calculations to make sure that the image is symmetrical. Video game graphics rely on the same techniques artists use to show depth and perspective.
Your Global Positioning System (GPS) also uses geometry to pinpoint your position in the world and lay out a path to get you to your destination. It uses satellites to locate you and then calculates the distance you are from those satellites. To do that, it must triangulate the data using the formulas for circles and spheres.
And these are only a few of the magical ways in which we use geometry, whether we know it or not! How do you use geometry? Tell us in the comments below. Interested in ensuring that your student explores geometry to its fullest potential? Take a free assessment with A Grade Ahead today!
Author: Susanna Robbins, Teacher and Franchise Assistant at A Grade Ahead
