Calculus 8A By: Laura Velez, Nicolas Hoyos, and Juan Nicolas Becerra

INtroduction

What Is calculus

Branch of mathematics concerned with the calculation of instantaneous rates of change and the summation of infinitely many small factors to determine some whole.

Sir Isaac Newton (1642-1727)

Newton discovered calculus between 1665 and 1667 after his university closed due to an outbreak of the Plague.

Newton was only 22 at the time, and he preferred not to publish his discoveries.

Meanwhile, in Germany, Leibniz discovered Calculus independently, he was very open with his findings. This led to a bitter dispute between the two mathematicians later known as the "Great Sulk".

Today it is well known that both men discovered calculus independently of the other, Leibniz about 8 years after Newton.

Newton is best known for his work in physics, and especially his three laws of motion.

"If I have made any valuable discoveries, it has been owing more to patient attention than to any other talents"-Newton

Gottfried Wilhelm Leibniz (1646-1716)

Though Leibniz is credited with discovering calculus after Newton he is the true founder of modern European mathematics.

He a great mathematician, philosopher, scientist, logician, diplomat and a lawyer.

Leibniz is well known for introducing notations that are still used in Calculus today, such as 'dy/dx' and the integral symbol. It is even attributed to him the '=' symbol, used throughout the world.

"It is rare to find learned men who are clean, do not stink, and have a sense of humour”- Leibniz

In perfect shape; the platonic solids

what are they?

Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.

Theory

According to Euclid (fl. c. 300 bc), the octahedron and icosahedron were first discussed by the Athenian mathematician Theaetetus (c. 417–369 bc).

However, the entire group of regular polyhedra owes its popular name to the great Athenian philosopher Plato (428/427–348/347 bc), who in his dialogue Timaeus associated them with the four basic elements—fire, air, water, and earth—that he supposed to form all matter through their combinations.

Plato assigned the tetrahedron, with its sharp points and edges.

To the element fire; the cube, with its four-square regularity.

To earth; and the other solids concocted from triangles (the octahedron and the icosahedron) to air and water, respectively.

To the regular polyhedra, the dodecahedron, with 12 pentagonal faces, Plato assigned to the heavens with its 12 constellations.

•Because of Plato’s systematic development of a theory of the universe based on the five regular polyhedra, they became known as the Platonic solids.

Explanation and Sketches

The tetrahedron is the Platonic solid with three triagular faces arranged around every vertex.

TETRAHEDRON

The cube is the Platonic solid with three square faces arranged around every vertex.

CUBE

The octahedron is the Platonic solid with four triangular faces arranged around every vertex.

OCTAHEDRON

The icosahedron is the Platonic solid with five triangular faces arranged around every vertex.

ICOSAHEDRON

The dodecahedron is the Platonic solid with three pentagonal faces arranged around every vertex.

DODECAHEDRON
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Created with images by stevepb - "coins calculator budget"

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