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TIME

in Maths

“C.D LOGA” National College

Pintilie Maria Gabriela

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—William L. Schaaf

“Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number Pi.”

Pintilie Maria Gabriela

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The history of PI

The value of π has been known for over 4000 years. The ancient Babylonians were the first to compute its value by multiplying 3 by the square of the radius of a circle, obtaining π =3. According to one Babylonian tablet, π has a value of 3.125.

The Rhind Papyrus provides insight into ancient Egyptian mathematics. The Egyptians estimated π to be 3.1605 by calculating the area of a circle using a formula that involved estimating the area of a square with sides that are 8/9 of the circle's diameter. Their estimation of π is only 0.6 percent greater than the most accurate value of π.

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History never ends…

Over the years, Chinese, Indian, and Arab mathematicians, rather than improving on Archimedes' method, they increased the number of decimal places known by laborious calculations. Chinese mathematician and astronomer Zu Chongzhi computed π as 3.14159292.

In Europe, Sir Isaac Newton calculated 16 decimal places using his binomial theory.

Early in the 20^th century, the Indian mathematician Srinivasa Ramanujuan discovered extremely efficient methods of computing π. Later on, his methods were incorporated into computer algorithms. Furthermore, in the early 21^st century, computers estimated the value of π =3.1415926535897.

The Greek letter π was introduced in the 1700s by William Jones, and it was popularized by Leonhard Euler.

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Gothic architecture

Space

Round Bridges

What will we talk about?

How were they designed?

The distances calculated from Earth

The mathematics known in the Roman Empire

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Gothic Architecture

Developed in Europe during the Middle Ages, the Gothic style was a spectacular representation of a new and more liberated religious spirit.

Medieval architects employed geometry as a tool structure to assemble thoughts and aesthetic impulses, or possibly to integrate a meaningful system of symbols into their work. In contrast to the Renaissance era, when achieving beauty or following the exact canonical models was paramount, they were more concerned with the inherent logic of the architecture.

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Pintilie Maria Gabriela

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Geometry is utilized as a visual tool in Gothic architecture to contemplate the mathematical nature of the Universe, which is closely tied to the Divine. The builders of the Middle Ages realized that the science of geometry that they utilized came from its creator, Euclid.

The most notable geometrical patterns are derived from the square within a circle (ad quadratum) and the triangle within a circle (ad triangulum), according to Euclidean hypotheses. With this in mind, all geometric design has a circle as its foundation, from which the pattern emerges.

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Bridges

The maths known in the Roman Empire

The ancient romans had a very advanced engineering technology for that time.They built their bridges with arches. When we talk about an arch, we automatically think of PI. But they didn’t, so what did they think of?

Pintilie Maria Gabriela

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Pintilie Maria Gabriela

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Gothic architecture

Space

Round Bridges

What will we talk about?

How were they designed?

The distances calculated from Earth

So the Romans didn’t really understand the maths and physics behind it all, it was just a trial and error process that gave us one of the most important engineering inventions. They didn’t know that you could calculate the radius of the arch in order to design the stones accordingly and therefor build the arches with no intermediate diffrences avoiding all the accidents that could happen. So the Romans were aproximately going by intuition, but of course the scientists discovered how you can exactly calculate all the data and avoid all errors, they just were some centuries too late…

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3,1415926

The eight first digits of the number Pi

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Calculating distances from earth

Space

Space, the great, big universe, needs PI to be discovered, as humans need air to breath.For example, you can calculate the lengh of orbits at different altitudes above a planet’s surface can be worked out by using the basic principle that if the diameter of a circle is known, its circumference can be calculated by multiplying by PI.

In 2015, NASA scientists applied this method to compute the time it took the spacecraft Dawn to orbit Ceres, a dwarf planet in the asteroid belt between Mars and Jupiter.

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So we see, even the most complicated things as the characteristics of untouched by humans planets are down to simple formulas and therefor down to PI, the best friend of mathematicians.

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Thank You!

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Bibliography

https://core.ac.uk/download/pdf/235442558.pdf

https://www.exploratorium.edu/pi/history-of-pi

https://www.britannica.com/science/pi-mathematics

https://www.jstor.org/stable/44571807

https://spaceplace.nasa.gov/saturn-rings/en/

“The Maths Book”

https://www.airedalesprings.co.uk/ancient-engineering-in-modern-times/

Pintilie Maria Gabriela