NEXT TIME you slice up a nice hot pizza don’t forget to add the quadratic equations. These will tell you how many pieces you can get from a given number of cuts.
And don’t be trapped into thinking that three cuts equals six slices and four cuts equals eight. Nobody said the slices all have to be the same size.
Few would bother to think quadratic equations as a prelude to a meal, but an Institute of Technology Tallaght lecturer in mathematics, Ciaran O’Sullivan, uses the idea to help students – and teachers – realise there are real-world applications that can help to explain why the equations are useful.
He gave a talk to teachers in Dublin yesterday evening as part of the ongoing Maths Week Ireland, entitled: “But what use is this algebra stuff in the real world?” He showed them exactly what quadratic equations could do for students and for dinner.
“Mathematics is a language of description,” he said yesterday, speaking before his talk. “It is a language for describing patterns and trends.” That, however, didn’t mean what you described had to be a bore.
Hence his use of pizza pie cutting as a way to encourage students to understand.
They are first given pictures of pizzas and allowed to draw lines representing cuts. Once they get past the notion that all pieces must be of equal size then it becomes like a puzzle.
“There is a pattern that emerges and you can link the number of pieces with the number of cuts,” he said.
That pattern boils down to a useful quadratic equation (write it down, it is a good one):
Pieces = 0.5x2+0.5x+1
where x is the number of cuts.
If you don’t want to do the sums, one cut will get you two pieces and two cuts gives four, but three cuts will yield seven pieces, four gives 11 and five will get you 16 individual – if uneven – pieces.
Mr O’Sullivan has come up with other diversionary tactics to make quadratics palatable such as tracking the trajectory of a volleyball pass and figuring out what size shock absorber you might need for an E-type Jaguar.
He does the same thing for “linear equations” by describing the work in the mid-1900s of noted forensic anthropologist Mildred Trotter. She developed a relationship linking a person’s height with various limb bones, including the femur and tibia in the leg and the humerus and radius in the arm. Moving back into the classroom, using skeletal remains to learn maths is much more interesting than plotting graphs and calculating slopes.
Her linear equation for calculating height using the femur is:
Height in cm=2.38 x (femur length in cm)+61.41
Mr O’Sullivan finds that students respond well to the approach. “It works because it is the first time they see these equations occurring in a natural process.”