Reveal the Beauty of Mathematics
Mathematics is full of drama, beauty, and emotion.
By Donna Iadipaolo
When you hear the word “math,” what comes to mind? Do you think “drill and kill”? Boring? Nerdy? Memorization? Plug and chug formulas? Calculators? Computers? Answers that are either right or wrong? You, as a teacher, may not think this way, but many of our students do. Our task, as educators, is to reveal mathematics as an often beautiful, wondrous, and even dramatic human endeavor that is a reward for our perseverance and diligence.
The Tale of Archimedes and Displacement
Take for instance the story of the ancient Greek mathematician Archimedes who discovered the principal of displacement. As the story goes, King Hieron II of Syracuse had commissioned a goldsmith to craft a crown from a hunk of gold. The king, however, thought that the goldsmith had taken some of the gold for himself and replaced it with silver. King Hieron II summoned Archimedes and asked him to prove whether his suspicion was true or not.
Archimedes thought long and hard, but was unable to come up with an immediate solution. According to the story, Archimedes went to take a bath and noticed that the water rose as he entered the tub. Excited and delighted by the idea of displacement, Archimedes then went running down the street naked shouting “Eureka!”
Solving a Math Problem Can Be Thrilling
Of course, I am not suggesting that students go running down the street naked upon discovering the solution to a challenging problem. But sharing such a story with students might help convey how thrilling and rewarding it is to make a discovery through careful observation of the world around us. As mathematician Shmuel Avital once wrote:
“To break the image of mathematics as a ‘boring’ subject we can add color and enliven it by considering its human side and from time to time expose students to anecdotes from the lives of mathematicians. In some cases, such anecdotes can even help solve educational problems.”
Eye of the Beholder
The beauty and elegance of mathematics may also be further explored in the classroom. Take, for instance, conic sections. The aesthetic of these shapes can be attributed to a large extent to their mathematical properties. In fact, when these shapes were first examined in 300 B.C. by Euclid, he studied them because of the sheer beauty of their inherent mathematics. It was only later that elliptical orbits or properties of projectile motion were discovered to be related to conic sections.
Students should be aware that many mathematicians experience aesthetic pleasures in their mathematical pursuits. At a minimum, math can be considered a creative activity, for many it is seen as an art form. While we often think of math as a natural counterpart to science, many also compare it to music or poetry in its elegance.
Bertrand Russell demonstrated his passion for mathematics when he stated:
“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.”
Some have even gone further to show how mathematics encompasses everything:
"Mathematics is the language with which God wrote the universe."
Here are some related lessons that may help explore the drama and beauty of math.
Math Lessons:
Students explore displacement. In this displacement and density lesson, students find the volume of irregular shaped objects. Afterwards, they determine the volume of containers. Students compute the amount of water displaced.
Students build a boat out of cardboard and tape. They apply Archimedes' Principle to their design
Students catapult grapes with a spoon and determine the mathematics of that event. The location of the grapes at various points of its flight path is charted to determine the curve of best fit.
Students relate the real-world application of an ambulance route to ellipses. They determine the equation of an ellipse given foci as well as other concepts pertaining to ellipses.
