What is Mathematikoi?

What is Mathematikoi?

Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagorean cult, who were considerably influenced by mathematics, music and astronomy. Pythagoreanism originated in the 5th century BC and greatly influenced Platonism.

What is Pythagorean wisdom?

Some even venture to believe that the word “philosophy” was invented by Pythagoras. He claimed to be a lover of wisdom, for which the Greek word philo means love and Sophia means wisdom. Pythagoras expressed his thoughts and ideas by using words and symbols rather than numbers as we know them today.

How did Pythagoras change the world?

In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus.

Can you only use Pythagorean theorem with right triangles?

Note that the Pythagorean Theorem only works with right triangles. You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle’s other two sides, called the legs.

What triangles use law of sines?

To use the Law of Sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an angle opposite one of them (SSA).

How is the law of sines proven?

Another way of stating the Law of Sines is: The sides of a triangle are proportional to the sines of their opposite angles. To prove the Law of Sines, let △ABC be an oblique triangle. In each case, draw the altitude from the vertex at C to the side ¯AB.

Is SSA law of sines?

“SSA” is when we know two sides and an angle that is not the angle between the sides. use The Law of Sines first to calculate one of the other two angles; then use the three angles add to 180° to find the other angle; finally use The Law of Sines again to find the unknown side.

How do you know if the law of sines has two solutions?

If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid.

Which type of problems can you use law of sines to solve?

It is valid for all types of triangles: right, acute or obtuse triangles. The Law of Sines can be used to compute the remaining sides of a triangle when two angles and a side are known (AAS or ASA) or when we are given two sides and a non-enclosed angle (SSA). We can use the Law of Sines when solving triangles.

What is ambiguous triangle?

The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides. The triangles resulting from this condition needs to be explored much more closely than the SSS, ASA, and AAS cases, for SSA may result in one triangle, two triangles, or even no triangle at all!

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