How has Leonhard Euler influenced geometry, math homework help

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Complete the DQ questions below between 80-90 words each question. For questions 2 and 4 reply back to post.

1. How has Leonhard Euler influenced geometry? Provide some examples of this contributions, which can include topics outside of geometry.

2. (Reply Back to this Post ex. i agree)Leonhard Euler is considered one of the greatest mathematicians of the 18th Century. He influenced geometry by treating trigonometric functions such as the angle formed by two sides of a triangle as numerical ratios and not lengths of lines. "While creating the Euler identity (eiθ = cos θ + i sin θ), with complex numbers (e.g., 3 + 2√(−1)), he discovered logarithms for negative numbers and showed that each complex number has an infinite number of logarithms". He also came up with notations when writing equations and labeling geometric shapes. For example, it was Euler who came up with labeling the sides of a triangle a, b, and c and each corresponding angle A, B, and C.

Euler was also known for his contributions to astronomy. He developed a more advanced theory of lunar motion as it related to the sun, moon, and earth. I found it particularly interesting that after he went blind, he was performing calculations in his head to come up with his second theory of lunar motion.

3.Provide an example of a geometric shape in nature. How does it benefit an object’s function?

4.(Reply Back to this Post ex. i agree) Many different ideas came to mind as I read this question. The main things I think of are traffic signs. Stop signs are octagons, yield signs are triangles, pedestrian/school crossing signs are pentagons, and some one way signs are rectangle shapes. Fruit, spider webs, and butterflies as well. When sliced some fruit can have a symmetry in each slice. Spider webs are complicated geometric designs, spiders create geometrically complex shapes. Butterflies wings show symmetry as well.

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Leonhard Euler’s influence on geometry
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1. How has Leonhard Euler influenced geometry? Provide some examples of this
contributions, which can include topics outside of geometry.
Euler was a Swiss mathematician who was very influential in the field of science
and geometry in the 18th century. He introduced the concept of mathematics which is now
referred to as Euler’s number. Euler also had great influence to geometry especially in the field
of graph theory which includes the traceability of a graph. In this case, he applied the theory
in solving the Konigsberg bridge problem. He also contributed to the use of the formula VE+F=2 which relates the numbers of the faces and vertices as well as the edges of a convex
polyhedron that led his characteristics. He also influenced a triangle the circumcentre which is
referred to as the center of the circumscribed circle. He also found the orthocenter which is the
point at which the perpendicular bisector of the sides meet. Moreover, he formulated the
centroid which is the place where the meridians meet. Moreover, he developed a proof
associating with radii of the circumcircle as well as in circle of the triangle. Moreover, he
developed the cosine and the sine. This defines the unit circle on the complicated number plane.
He elaborated the theory of the high transcendental functions using gamma
functions. He was able to introduce a new metho...

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