The Pythagorean Theorem was named after the Greek mathematician Pythagoras. He has made a statement in geometry which shows the relationship between the lengths of any right-angled triangle. Therefore, the area of the square built upon the hypotenuse of a right triangle, square c, is equal to the sum of the areas of the squares upon the remaining sides, a and b, (see Figure 1). The theorem can be written as a2+b2=c2, where c is the length of the hypotenuse while a and b are the lengths of the other two sides. Whilst the theorem may have been first proven by Pythagoras it was discovered that Babylonian mathematicians knew about the theorem over 1,000 years before the Greek mathematician’s time.

Figure 1 Geometrical representation of the Pythagorean theorem.

Pythagoras theorem can be applied in real life to several fields listed below:


• Architecture: by calculating the diagonal length of a sloped roof or the size of the beam supporting the roof

Figure 2 representation of Pythagoras theorem in architectural works.

 The Pythagorean Theorem is also used in laying out square angle.


Meteorologists and Aerospace engineers, by determining the range of sound and from where it originates.

Figure 3 demonstrates a radar collecting data analyzed using Pythagorean Theorem and weather station estimating clouds distance.


Surveying: by calculating the numerical distances and heights between different points before creating a map.

Figure 4 shows application of Pythagoras theorem in survey jobs.

Navigation, the navigators often use the theory to estimate the distance between two points. For example, if an individual wants to navigate between two points that are 500 miles east and 800 miles west, the theorem can be used to estimate the distance of the ship to that destination. The distances east and west will indicate the two points of the triangle while the shortest part that connects the two legs of the diagonal. Pilots can use the theorem to estimate the descent point. For instance, the plane can use the distance from the destination airport and its height from the ground to find the correct point from which it can begin to ascend.

Figure 5 represents application of Pythagoras theorem in aircraft navigation.


Oceanographers by determining the speed of sound in water and the direction it is produced from.

Figure 6 represents use of Pythagoras theorem in sea adventures.

 The Pythagorean Theorem is said to have one of the most significant numbers of proofs in the mathematics discipline. Proofs range from using algebra, pure geometry or even calculus by using differentials. By using the Pythagorean Theorem, we can also arrive at the converse theorem that states that for any numbers a, b and c with a2+b2=c2 then a triangle can exist with the equivalent sides and a 90 degree angle between a and b.


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O’Connor, J. and Robertson, E., 2020. Babylonian Pythagoras. [online] Maths History. Available at: <> [Accessed 24 October 2020].

BYJUS., 2020. Pythagorean Theorem Formula, Derivation, And Solved Examples. [online] Available at: <> [Accessed 22 October 2020].

O’Connor, J. and Robertson, E., 2020. Babylonian Pythagoras. [online] Maths History. Available at: <> [Accessed 24 October 2020]., 2020. Pythagorean Theorem. [online] Available at: <> [Accessed 25 October 2020].

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