Euclid, in his mathematical treatise Elements, proposed that irrational square roots are also possible. However, because the ancient Greeks did not use the same number system that we now use, it was not possible to calculate the square root by hand, which is what architects and engineers really needed. Indian mathematics used the decimal system. It also had one other advantage over the system used by the ancient Egyptians and Greeks — the zero. Zero allowed mathematicians to not only theorize about irrational numbers but to use them in equations.
Brahmagupta recognized that there are two roots in the solution to a quadratic equation and described the quadratic formula as, "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value.
This was also one of the first works to describe concrete ways of using zero. He solved the quadratic equation using algebraic expressions although he rejected negative solutions and is often credited as the father of algebra. His work made its way to Europe by around AD, where it was translated into Latin. By , Italian scientist Gerolamo Cardano had compiled works related to the quadratic equations, including both Al-Khwarizmi's solution and Euclidean geometry.
In his works, he allows for the existence of roots of negative numbers. Flemish engineer and physicist Simon Stevin gave the general solution of the quadratic equation for all cases in his book Arithmetic in the year Descartes's work included the quadratic formula in the form we know today. Quadratic equation came into existence because of the simple need to conveniently find the area of squared and rectangular bodies, but from the days of its origin, this popular maths equation has now come a long way to prove its significance in the real world.
For example a softball, tennis ball, football, baseball, soccer ball, basketball, etc. It also used to design any object that has curves and any specific curved shape needed for a project. The military uses the quadratic equation when they want to predict where artillery shells hit the earth or target when fired from cannons. So if your goal is to go into the military and work with artillery or tanks, you will be using the quadratic equation on a daily basis.
Other uses of the quadratic equation include explaining how planets in our solar system revolve around the sun. Our planets were initially tracked by early scientists, who did not have the advantage of computers, and they used the quadratic equation to determine how planets in our solar system do not have circular orbits - they have elliptical orbits. Newton also based his laws of motion on the quadratic equation by defining the acceleration of objects and forces that act upon them.
Answering the more general question, I think learning about history is the best way to have these kinds of answers. Almost every mathematical construct taught at college level was either devised to solve a practical problem, found applicability in various domains once it was found, or at the very least has some interesting backstory preceding or following its discovery. All of these help give some concrete context to the abstract mathematics. Of course have in mind that being able to answer these questions will probably not solve your students' interest issues by itself!
I'll try to answer your question from another point of view. To me, it's important not to know how to solve quadratic equations, but to show your students that they already know how to do that.
Did your student have to know anything to come up with this conclusion? No, he already knew that. And that's the point of math — it can be treated as an art of arriving at unexpected conclusions by reflecting on the things you already know. Quadratics just serve as a simple example of that approach to make sure your students get the general idea.
I remember this exact question from every math class I've ever been in. After having kids and thinking more about why the question was asked I found that the best answer is this: Mathematics is a method for explaining and finding solutions to not only problems, but the very foundation of everything that exists.
No your students will probably never have to use the quadratic formulae unless they become chemists or some such field, however understanding that the formulas they learn apply to everyday life and the world around them will help them better understand the whys and hows of reality. There is no other way that is not conjecture. Math is fact. Sign up to join this community. The best answers are voted up and rise to the top.
Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why we need to know how to solve a quadratic? Ask Question. Asked 9 years, 3 months ago. Active 2 years, 4 months ago. Viewed 17k times. One of them asked me the following question when I tried to ask him to solve a quadratic: Why do I need how to solve a quadratic?
I am not going to use it for my future job! Bombyx mori Bombyx mori What is the importance of knowing Tokio is Japan's capital city? Well, for one, knowing stuff is fun and rewarding for many people, and for two: if you're about to be a teaching assistany and you still cannot give a good reason to a mathematics student why quadratics are important then I'm afraid you may not be ready for that post. Oh, and of course: for people not dealing with mathematics the answer is easy: solving quadratic is good for nothing, and they don't even give you milk for one Quadratic equations are often used by the military or law enforcement to determine the speed of moving objects such as cars and planes.
The military can also use them to determine the distance between them and an approaching enemy. In addition, the military uses quadratic equations to predict where tanks or artillery will land. The police apply it when figuring out the trajectories of bullets.
The traffic police use it to figure out the speeds of cars involved in accidents on the road. Engineers apply quadratic equations more than any other career. Quadratic equations are important when designing curved equipment such as auto-bodies. Brake systems are designed by automotive engineers by solving equations that arise.
Aerospace engineers also interact with quadratic equations so often in their careers. Chemical and electrical engineers deal with quadratic equations daily because they work with complex systems. Audio engineers design sound systems with the help of solving some equations. There are thousands of management and clerical work that involve the use of quadratic equations daily. For example production, managers and engineering managers supervise people that are dealing with equations.
That means they need to have solid knowledge on the same. Human resource managers have to determine the workforce cable of completing some given tasks. In addition, they have to figure out how to pay or design pension plans.
All those activities actively depend on the quadratic equations. Insurance agents also deal with them because they have to design complex insurance models and plans that involve a lot of computation.
Quadratic equations are also applied in agriculture extensively. Without agriculture, human beings cannot survive. So that means that these equations play a major role in the existence of the human race. One of the biggest applications of quadratic equations in Agriculture is in the arrangement of boundaries. For example, calculating the areas of pens that will produce high yields involves finding the areas.
Some area calculations lead to the formation of an equation.
0コメント