# No. 2983: IN DEFENSE OF QUADRATIC EQUATIONS

by Andrew Boyd

**Click here for audio of Episode 2983**

Today, the British Parliament speaks out. The University of Houston’s College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

It was a topic of such magnitude that in 2003 the British Parliament took it up for debate. At issue were public comments made by the head of the schoolteachers’ union. The union head asked why students were being taught irrelevant topics, and as an example pointed to … quadratic equations. Official records of the parliamentary debate appear under the simple yet apt title “Quadratic Equations.”

In his opening statement, Parliamentary Member Tony McWalter described quadratic equations to his colleagues thusly: “[Quadratic equations] have only one unknown expression but they allow it to be raised to a power of 2, for example x^{2} = 4 … Another example is 3x^{2} + x - 10 = 0.”

*Quadratic Equation*. * Photo Credit: Andy Boyd*

Students world over can recount their experiences with quadratic equations and memorizing the infamous quadratic formula. Which leads us to ask, why *should* students care about quadratic equations?

*Quadratic Formula*. * Photo Credit: Andy Boyd*

Imagine a rancher who knows he needs two acres of pastureland to raise one head of cattle. If he wants to fence off a square region for 20 head, how much fencing does he need? The answer comes from a quadratic equation.

Problems like the rancher’s were common as early as 2000 BC in Babylonia, and clay tablets dating to that period show the Babylonians used what was essentially the quadratic formula to solve them. And throughout history many different cultures dealt with quadratic equations long before the Greeks got their hands on them. Egypt. China. India. Quadratic equations kept popping up because they solved so many practical problems.

Much later, in the sixteenth century, Galileo made the monumental discovery that the distance an object falls over time is described by a quadratic equation. The motions of the planets — an almost obsessive topic with scholars over the millennia — are described by quadratic equations. So is the arc formed by a baseball as it travels through the air.

And that’s why the honorable Mr. Tony McWalter stood before the House of Commons in defense of “mathematics in general [and] quadratic equations in particular.” And in an entertaining yet serious commentary, he invoked name after name of prominent engineers and scientists who had connections with quadratic equations.

“Hear, hear” cried the lone voice of the honorable Mrs. Eleanor Laing.

“Oh dear,” replied McWalter. “I would like to have support from elsewhere as well.”

As the debate wound down, it was the honorable Alan Johnson, Minister for Lifelong Learning, Further and Higher Education, who had the last word. Quoting none other than Napoleon Bonaparte, he shared a brutally practical interpretation of the importance of math: “The advancement and perfection of mathematics are intimately connected with the prosperity of the state.”

To which I can only add, “hear, hear.”

*McWalter's Statement on the Quadratic Formula.* * Photo Credit: Andy Boyd*

I’m Andy Boyd at the University of Houston, where we’re interested in the way inventive minds work.

(Theme music)

The record of the debate can be found in Hansard, United Kingdom House of Commons, 26 June 2003, Columns 1259-1269, 2003. See also http://www.parliament.the-stationery-office.co.uk/pa/cm200203/cmhansrd/vo030626/debtext/30626-20.htm. Accessed January 3, 2015. The debate begins near the bottom of the page. The full context of the debate — its “entertaining yet serious” quality — is best appreciated from a reading of the transcript itself.

C. Budd and C. Sangwin. 101 Uses of a Quadratic Equation. From the *+plus magazine website*: http://plus.maths.org/content/os/issue29/features/quadratic/index. Accessed January 3, 2015.

C. Budd and C. Sangwin. 101 Uses of a Quadratic Equation: Part II. From the *+plus magazine* website: http://plus.maths.org/content/101-uses-quadratic-equation-part-ii. Accessed January 3, 2015.

J. O'Connor and E. Robertson. An Overview of Babylonian Mathematics. From the University of Saint Andrews MacTutor History of Mathematics Archive: http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_mathematics.html. Accessed January 3, 2015.

Quadratic Equation. From the Wikipedia website: http://en.wikipedia.org/wiki/Quadratic_equation#History. Accessed January 3, 2015.

This episode first aired on January 8, 2015.