WHAT IS PYTHAGOREAN THEOREM AND ITS APPLICATION IN REAL LIFE ?
Abstract |
An introduction to the pythagorean theorem,history and life applications.
Have you ever heard of the Pythagorean Theorem in class or in a Youtube Video? Do you know what is it about?
In Mathematics,Pythagorean theorem is a fundamental relation in Euclidean Geometry among the three sides of a right triangle.It states that “In a right-angled triangle,the square of the hypotenuse side,which is the longest side,is equal to the sum of squares of the other two sides.”
Now,let me share with you about the history of the Pythagorean theorem!
The Pythagorean theorem is one of the important mathematical theorems discovered and proved in the early days of mankind.However,it was known more than a thousand years earlier.Other than that,it is also one of the most important tools in solving geometric problems with algebraic thinking and one of the links between numbers and shapes.
In China,Shang Gao of the Zhou Dynasty proposed a special case of the “three strands,four strings and five” to prove the Pythagorean theorem.
In the West,the first person to propose and prove this problem was the Pythagoras school of ancient Greece in the 6th century BC.They proved deductively that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two right angles.
How did Pythagoras discovered this concept?There are many legends about that.This theorem is discovered by Pythagoras himself.The chance was that when he visited a friend’s house one day,he saw the slate laid in the courtyard.The area of the square on the hypotenuse of an isosceles right triangle is equal to the sum of the areas of the two squares on both sides of the right angle.It’s said that since Pythagoras noticed this,he only worked on the right triangle.However,it is unclear whether this claim is true.Another method is Pythagoras learned from the Egyptians that 3+4=5,and in the triangle formed by the three sides of 3,4 and 5,one of the corners will be a right triangle.Perhaps this statement is more correct.In addition,a book even records that when Pythagoras discovered this theorem,he danced with joy and thanked the Muses(the general term of the goddess of art and science in Greek mythology).
Discovered by research,an ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurately the right angles for surveying land.
Pythagoras,Greek Mathematician and Philosopher
Thus,how many ways to prove Pythagoream Theorem?
Proven of Pythagorean Theorem by 11-year-old Einstein
i) Divide one right triangle into two others and uses the principle that if the corresponding angles of two triangles are the same.
ii) The ratio of areas of the three triangles is equal to the ratio of the squares of the sides.Draw a square on the hypotenuse of each triangle.
iii) Now,if we need to calculate the area of each square,the square will become a²,b² and c².
iv) Suppose that the areas of the triangle and rectangle are xa²+xb²=xc².
∴a²+b²=c²
2. Proof of Rearrangement
(b-a)²+4 x 1/2ab =c²
Now,expand and solve it!
b²-2ab+a²+2ab=c²
∴a²+b²=c²
Pythagorean Theorem : Real Life Application
Example
When decorating the house,in order to judge whether a corner is a standard right angle,workers can measure 30cm and 40cm from the corner to the two walls and mark it at a point,and then measure whether the distance between the two points is 50cm.If it exceeds a certain interval,then it means that the corners are not the right angles.For instance,point A has a high pole near it and point B should fix the rope drawn from the top of the pole at this point.So,we can calculate the length of the rope required.
2. We can use the Pythagorean theorem and two lengths to find the shortest distance.For example,if you are sailing at sea to a point 300 miles north and 400 miles west,you can utilise this theorem to find your ship’s distance to that point,and calculate how many degrees north and west you will need to follow to get to that point.The same principle can be used for air navigation.For instance,an aircraft can use its height above ground and distance from the airport to find the correct location to start descending to that airport.
3. Pythagoras Theorem is used extensively in architecture and construction.Given two straight lines,the Pythagorean theorem allows us to calculate the length of the diagonal connecting them.This application is often used for construction,carpentry or other physical construction projects.
[ All in all,the Pythagorean Theorem is one of the very vital formula in the world of mathematics.When we dealing with right triangles,the Pythagorean relation effectively helps to study length measures and establish the relationship between the three sides of a right triangle.In our daily life,people always use the Pythagorean theorem for trigonometric ratios and measurements of height and distance as well as in construction and so on.]
Reference:
https://sciencing.com/real-life-uses-pythagorean-theorem-8247514.html
AUTHOR
GOH YING HANG
My name is Goh Ying Hang.I am from Batu Pahat Tigs.Math has played a vital role in my life.It gives me the ability to think logically and critically about the world around us.Let's love mathematics and explore the wonderful world together!
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