Explain & History of Theorem of Pythagoras. What is your knowledge of Pythagoras’ theorem? Despite the fact that the theorem has been in existence for centuries, its relevance and application remain as relevant today as ever.
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Introduction:
There is no doubt that the Pythagorean Theorem is one of the most important and famous theorems in mathematics. It was discovered by the ancient Greek mathematician Pythagoreus in the 6th century BC and is still used today in mathematics, physics, engineering, and architecture.
Throughout history, this remarkable theorem has been used to solve a wide variety of problems as well as to solve the theorem’s long and fascinating history.
What is Pythagoras?
Pythagoras was a Greek philosopher, mathematician, and the founder of Pythagoreanism, a philosophical and religious movement. He is best known for his contributions to geometry, specifically for his famous theorem.
History of the Pythagoras theorem
A Greek mathematician named Pythagoras proved Pythagores’ theorem over 2,500 years ago, making it one of the oldest and most famous theorems in mathematics. In right-angled triangles, the squares of the two shorter sides equal the squares of the longest sides.
Statement of Pythagoras’ theorem
Essentially, the Pythagoras theorem states that the square of the hypotenuse (the longest side) equals the sum of the squares of the two other sides of a right-angled triangle.
The equation a2 + b2 equals c2 .
Example:
Taking a look at a triangle with lengths of 3, 4, and 5, let us see how this theorem can be applied. By using the Pythagorean theorem, it is possible to calculate that the square of the hypotenuse (the side that is opposite the right angle) is equal to the square of the other two sides. We can do this by using the equation: 32 + 42 = 52.
Based on this equation, the hypotenuse of a right-angled triangle is 5, which is equal to the square root of 25 (32 + 42). You can see from this theorem that it can be applied to a wide range of applications to calculate the hypotenuse length in a right-angled triangle.
Derivation of Pythagorean Theorem Formula
The Pythagorean theorem can be derived from the geometry of a right-angled triangle. The triangle is formed by two acute angles and one right angle. The right angle is formed by the two sides that cross at that angle.
From the two shorter sides of the triangle, A can be calculated if their measurements are a and b. Therefore, the hypotenuse’s measurement is c. Based on these lengths, we can determine the length of A.
Now, if the area of the triangle is equal to the square of the hypotenuse, then the formula for the Pythagorean theorem is derived. This is done by substituting the value of the area in the equation: A = 1/2*a*b = c². This equation can then be rearranged to give the equation: a² + b² = c².
Formula
Pythagoras’ Theorem can be expressed as a2 + b2 = c2, where both a and b represent known parts of the triangle, and c represents the unknown part.
According to the theorem, the hypotenuse’s square (the side opposite the right angle) equals the sum of the sides.
Applications of Pythagoras Theorem
There are a number of applications of this theorem, ranging from architecture and engineering to mathematics, physics, and astronomy.
In architecture
Architects and engineers use the Pythagorean theorem to determine the dimensions of a triangle, whether it is a right-angled triangle or a right triangle, or an oblique triangle. The theorem can also be used to compute the area of a triangle, which can be applied to any figure or shape.
In mathematics
A Pythagorean theorem can be used to determine the length of the sides of a triangle and to solve quadratic equations. This theorem is also used to calculate the area of a triangle, which can be used to calculate the area of any figure or shape. Also, it can be used to solve equations involving circles and triangles.
In physics
To calculate the speed of light, the Pythagorean theorem is also used to determine the force of gravity between two masses by taking into account the speed of light in a vacuum. In addition to calculating acceleration due to gravity, this formula is also used to determine a body’s change in velocity when it falls toward a planet as a result of gravity’s gravitational pull.
In engineering
The Pythagorean Theorem is used to calculate the forces and moments in trusses and other structures. The theorem is also used to calculate the angle of incline of a surface with respect to a horizontal plane.
In astronomy
In astronomy, the Pythagorean theorem is employed to calculate the distances between stars and galaxies, the orbits of planets in the solar system, and the positions of celestial bodies in the night sky.
FAQs
Is the Pythagorean Theorem still used today?
It is true that the Pythagorean theorem is still widely used today in various fields. It is one of the most important results in mathematics, and its applications are still relevant in many different fields today.
Conclusion:
It is a simple, yet powerful mathematical method of solving many problems. As a result of its simple and elegant formula, it is an invaluable asset to any mathematician or scientist. Its principles are widely used in many areas, including geometry, physics, engineering, and a wide range of others.
