Archimedes Plutonium

2017-06-14 14:53:39 UTC

Ancient Greeks, it was Euclid's Elements, by 2017 it is AP's ARRAY

ARRAY of MATHEMATICS, governed by Conservation of Proof Principle

Each line is a data, or fact or theorem of mathematics. Some lines are Comments

Comment_p_i::

Comment_p_j::

Fact_k::

Statement_r_u::

Fact:: First known use of Pythagorean theorem was with Babylonian and Egypt math using 3,4,5 as a tool in building.

....,

....,

S_i

S_i+1

....,

....,

....,

S_j

S_j+1

....,

Statement of Pythagorean Theorem, given any right-triangle with sides a, b, c, that we have

a^2 +b^2 = c^2

....,

....,

Proof of PT::

Picture proof

a b

L 1 K

c

c

2

4

c c

I 3 J

b a

then

L a K

b b a

I b J

Comment:: Notice the length of the statement of theorem is about equal length as the proof-statement.

Fact: the Thales theorem or called Inscribed Angle theorem is that the triangle inside a circle with one side as diameter of circle always generates a right triangle. This theorem is one of the oldest proven theorems in math history. We have history data of its proof by Thales. And is a theorem that forges a path to the trigonometry from the unit circle with right triangles whirling around inside the unit circle. When we adapt the theorem to the radius instead of diameter

Statement-theorem:: You have a circle O with center at P and points A, B, C where AC is the diameter, then the angle at ABC as seen in picture below as v+u, is a 90 degree angle.

Proof-Statement:: Connect PB thus two triangles ABP and PBC. Since AP, PB, PC are all equal as radii, the two triangles are isosceles. The base angles are equal. Picture::

B

v u

A v P u C

v + (v+u) + u = 180

2v + 2u = 180

v+u = 90

Comment:: In the early history of mathematics, theorems of math with a deductive proof show up at the time of the Ancient Greeks, Thales being one of the earliest.

Data:: A history timeline goes like this::

Thales of Miletus 624-546 BC magnetism and Thales theorem about inscribed triangle in circle, and a precursor of Atomic theory only with arche-- water.

Pythagoras of Samos 570-495 BC

Theaetetus Athens 417- 369 BC

Democritus, Abdera Thrace, 460 - 370 BC Atomic theory

Plato Athens 426-347 BC theory that four solids of matter correspond to four elements and 5th is the universe-ether as a dodecahedron

Euclid Alexandria 360- 270 ?? BC his textbook Elements would become history's first Deductive and Logical Science and based on the 5 only existing regular polyhedra as a model. The term "Elements" comes from the Greek meaning guiding principle.

Archimedes 287 - 212 BC

(sources mostly Wikipedia)

According to Proclus, the term "element" was used to describe a theorem that is all pervading and helps furnishing proofs of many other theorems.

Comment:: Euclid was Ancient Greek but now in 2017 we start a new fresh encyclopedia on mathematics and I chose to call it the ARRAY, where not one theorem is a guiding principle, but rather a Conservation Principle as the guiding light for the Array. This means that proofs are of almost equal size as the theorem statement.

....,

Statement-Theorem:: There can Only Exist 5 Regular Polyhedra

Comment:: When you fully define these regular Polyhedra, that takes up a lot of space. And the proof of that statement will be of approx. equal size.

....,

S_k

S_k+1

....,

....,

Fundamental Theorem of Arithmetic

Fundamental Theorem of Calculus

Fundamental Theorem of Algebra

Comment:: now the order of the ARRAY is desirable to be of a history order. But, in many cases, we can lump and repeat statements. Remember, the ARRAY is going to be huge. I am talking of volumes that would fill a entire library, just on math ARRAY. And of course, in our computer age, we have the ARRAY accessible by computer.

.....,

AP

ARRAY of MATHEMATICS, governed by Conservation of Proof Principle

Each line is a data, or fact or theorem of mathematics. Some lines are Comments

Comment_p_i::

Comment_p_j::

Fact_k::

Statement_r_u::

Fact:: First known use of Pythagorean theorem was with Babylonian and Egypt math using 3,4,5 as a tool in building.

....,

....,

S_i

S_i+1

....,

....,

....,

S_j

S_j+1

....,

Statement of Pythagorean Theorem, given any right-triangle with sides a, b, c, that we have

a^2 +b^2 = c^2

....,

....,

Proof of PT::

Picture proof

a b

L 1 K

c

c

2

4

c c

I 3 J

b a

then

L a K

b b a

I b J

Comment:: Notice the length of the statement of theorem is about equal length as the proof-statement.

Fact: the Thales theorem or called Inscribed Angle theorem is that the triangle inside a circle with one side as diameter of circle always generates a right triangle. This theorem is one of the oldest proven theorems in math history. We have history data of its proof by Thales. And is a theorem that forges a path to the trigonometry from the unit circle with right triangles whirling around inside the unit circle. When we adapt the theorem to the radius instead of diameter

Statement-theorem:: You have a circle O with center at P and points A, B, C where AC is the diameter, then the angle at ABC as seen in picture below as v+u, is a 90 degree angle.

Proof-Statement:: Connect PB thus two triangles ABP and PBC. Since AP, PB, PC are all equal as radii, the two triangles are isosceles. The base angles are equal. Picture::

B

v u

A v P u C

v + (v+u) + u = 180

2v + 2u = 180

v+u = 90

Comment:: In the early history of mathematics, theorems of math with a deductive proof show up at the time of the Ancient Greeks, Thales being one of the earliest.

Data:: A history timeline goes like this::

Thales of Miletus 624-546 BC magnetism and Thales theorem about inscribed triangle in circle, and a precursor of Atomic theory only with arche-- water.

Pythagoras of Samos 570-495 BC

Theaetetus Athens 417- 369 BC

Democritus, Abdera Thrace, 460 - 370 BC Atomic theory

Plato Athens 426-347 BC theory that four solids of matter correspond to four elements and 5th is the universe-ether as a dodecahedron

Euclid Alexandria 360- 270 ?? BC his textbook Elements would become history's first Deductive and Logical Science and based on the 5 only existing regular polyhedra as a model. The term "Elements" comes from the Greek meaning guiding principle.

Archimedes 287 - 212 BC

(sources mostly Wikipedia)

According to Proclus, the term "element" was used to describe a theorem that is all pervading and helps furnishing proofs of many other theorems.

Comment:: Euclid was Ancient Greek but now in 2017 we start a new fresh encyclopedia on mathematics and I chose to call it the ARRAY, where not one theorem is a guiding principle, but rather a Conservation Principle as the guiding light for the Array. This means that proofs are of almost equal size as the theorem statement.

....,

Statement-Theorem:: There can Only Exist 5 Regular Polyhedra

Comment:: When you fully define these regular Polyhedra, that takes up a lot of space. And the proof of that statement will be of approx. equal size.

....,

S_k

S_k+1

ARRAY of MATHEMATICS, governed by Conservation of Proof Principle

Each line is a data, or fact or theorem of mathematics. Some lines are Comments

Comment_p_i::

Comment_p_j::

Fact_k::

Statement_r_u::

Fact:: First known use of Pythagorean theorem was with Babylonian and Egypt math using 3,4,5 as a tool in building.

....,

....,

S_i

S_i+1

....,

....,

....,

S_j

S_j+1

....,

Statement of Pythagorean Theorem, given any right-triangle with sides a, b, c, that we have

a^2 +b^2 = c^2

....,

....,

Proof of PT::

Picture proof

a b

L 1 K

c

c

2

4

c c

I 3 J

b a

then

L a K

b b a

I b J

Comment:: Notice the length of the statement of theorem is about equal length as the proof-statement.

Fact: the Thales theorem or called Inscribed Angle theorem is that the triangle inside a circle with one side as diameter of circle always generates a right triangle. This theorem is one of the oldest proven theorems in math history. We have history data of its proof by Thales. And is a theorem that forges a path to the trigonometry from the unit circle with right triangles whirling around inside the unit circle. When we adapt the theorem to the radius instead of diameter

Statement-theorem:: You have a circle O with center at P and points A, B, C where AC is the diameter, then the angle at ABC as seen in picture below as v+u, is a 90 degree angle.

Proof-Statement:: Connect PB thus two triangles ABP and PBC. Since AP, PB, PC are all equal as radii, the two triangles are isosceles. The base angles are equal. Picture::

B

v u

A v P u C

v + (v+u) + u = 180

2v + 2u = 180

v+u = 90

Comment:: In the early history of mathematics, theorems of math with a deductive proof show up at the time of the Ancient Greeks, Thales being one of the earliest.

Data:: A history timeline goes like this::

Thales of Miletus 624-546 BC magnetism and Thales theorem about inscribed triangle in circle, and a precursor of Atomic theory only with arche-- water.

Pythagoras of Samos 570-495 BC

Theaetetus Athens 417- 369 BC

Democritus, Abdera Thrace, 460 - 370 BC Atomic theory

Plato Athens 426-347 BC theory that four solids of matter correspond to four elements and 5th is the universe-ether as a dodecahedron

Euclid Alexandria 360- 270 ?? BC his textbook Elements would become history's first Deductive and Logical Science and based on the 5 only existing regular polyhedra as a model. The term "Elements" comes from the Greek meaning guiding principle.

Archimedes 287 - 212 BC

(sources mostly Wikipedia)

According to Proclus, the term "element" was used to describe a theorem that is all pervading and helps furnishing proofs of many other theorems.

Comment:: Euclid was Ancient Greek but now in 2017 we start a new fresh encyclopedia on mathematics and I chose to call it the ARRAY, where not one theorem is a guiding principle, but rather a Conservation Principle as the guiding light for the Array. This means that proofs are of almost equal size as the theorem statement.

....,

Statement-Theorem:: There can Only Exist 5 Regular Polyhedra

Comment:: When you fully define these regular Polyhedra, that takes up a lot of space. And the proof of that statement will be of approx. equal size.

....,

S_k

S_k+1

....,

....,

Fundamental Theorem of Arithmetic

Fundamental Theorem of Calculus

Fundamental Theorem of Algebra

Comment:: now the order of the ARRAY is desirable to be of a history order. But, in many cases, we can lump and repeat statements. Remember, the ARRAY is going to be huge. I am talking of volumes that would fill a entire library, just on math ARRAY. And of course, in our computer age, we have the ARRAY accessible by computer.

.....,

AP

ARRAY of MATHEMATICS, governed by Conservation of Proof Principle

Each line is a data, or fact or theorem of mathematics. Some lines are Comments

Comment_p_i::

Comment_p_j::

Fact_k::

Statement_r_u::

Fact:: First known use of Pythagorean theorem was with Babylonian and Egypt math using 3,4,5 as a tool in building.

....,

....,

S_i

S_i+1

....,

....,

....,

S_j

S_j+1

....,

Statement of Pythagorean Theorem, given any right-triangle with sides a, b, c, that we have

a^2 +b^2 = c^2

....,

....,

Proof of PT::

Picture proof

a b

L 1 K

c

c

2

4

c c

I 3 J

b a

then

L a K

b b a

I b J

Comment:: Notice the length of the statement of theorem is about equal length as the proof-statement.

Fact: the Thales theorem or called Inscribed Angle theorem is that the triangle inside a circle with one side as diameter of circle always generates a right triangle. This theorem is one of the oldest proven theorems in math history. We have history data of its proof by Thales. And is a theorem that forges a path to the trigonometry from the unit circle with right triangles whirling around inside the unit circle. When we adapt the theorem to the radius instead of diameter

Statement-theorem:: You have a circle O with center at P and points A, B, C where AC is the diameter, then the angle at ABC as seen in picture below as v+u, is a 90 degree angle.

Proof-Statement:: Connect PB thus two triangles ABP and PBC. Since AP, PB, PC are all equal as radii, the two triangles are isosceles. The base angles are equal. Picture::

B

v u

A v P u C

v + (v+u) + u = 180

2v + 2u = 180

v+u = 90

Comment:: In the early history of mathematics, theorems of math with a deductive proof show up at the time of the Ancient Greeks, Thales being one of the earliest.

Data:: A history timeline goes like this::

Thales of Miletus 624-546 BC magnetism and Thales theorem about inscribed triangle in circle, and a precursor of Atomic theory only with arche-- water.

Pythagoras of Samos 570-495 BC

Theaetetus Athens 417- 369 BC

Democritus, Abdera Thrace, 460 - 370 BC Atomic theory

Plato Athens 426-347 BC theory that four solids of matter correspond to four elements and 5th is the universe-ether as a dodecahedron

Euclid Alexandria 360- 270 ?? BC his textbook Elements would become history's first Deductive and Logical Science and based on the 5 only existing regular polyhedra as a model. The term "Elements" comes from the Greek meaning guiding principle.

Archimedes 287 - 212 BC

(sources mostly Wikipedia)

According to Proclus, the term "element" was used to describe a theorem that is all pervading and helps furnishing proofs of many other theorems.

Comment:: Euclid was Ancient Greek but now in 2017 we start a new fresh encyclopedia on mathematics and I chose to call it the ARRAY, where not one theorem is a guiding principle, but rather a Conservation Principle as the guiding light for the Array. This means that proofs are of almost equal size as the theorem statement.

....,

Statement-Theorem:: There can Only Exist 5 Regular Polyhedra

Comment:: When you fully define these regular Polyhedra, that takes up a lot of space. And the proof of that statement will be of approx. equal size.

....,

S_k

S_k+1