What’s so difficult about Pi? │ The History of Mathematics with Luc de Brabandère
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- Опубліковано 7 лип 2024
- The constant Pi is one of the world’s oldest enigmas.
Extremely difficult to define exactly, its trillion-digit decimal sequence has confounded mathematicians for centuries.
#Mathematics #Science #PI #Maths
Philosopher Luc de Branbandère guides us through the history of mathematics, from Egyptians measuring with the Sun to modern algorithms for self-driving cars.
Find out more:
www.piday.org
lucdebrabandere.com/
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Some of the properties of the Kepler right triangle:
The measuring angles for the hypotenuse of a Kepler right scalene triangle are 51.82729237298776 degrees and 38.17270762701224 degrees in Trigonometry.
51.82729237298776 degrees is gained when the ratio 1.272019649514069 is applied to the inverse of the Tangent function in Trigonometry.
38.17270762701226 degrees is gained when the ratio 0.786151377757423 is applied to the inverse of the Tangent function in Trigonometry.
If the hypotenuse of a Kepler scalene right triangle is divided by the shortest edge length of the Kepler scalene right triangle then the resulting ratio is the Golden ratio of Cosine (36 degrees) multiplied by 2 = 1.618033988749895.
1.27201964951406 is the ratio gained from dividing the second longest length of a Kepler scalene right triangle by the shortest edge length of the Kepler right scalene triangle.
1.27201964951406 is also the square root of the Golden ratio of Cosine (36 degrees) multiplied by 2 = 1.618033988749895.
The Kepler right triangle is the solution to:
1. Discovering the correct value for Pi = 4/√φ = 3.144605511029693144.
2. Creating a circle and a square with the same surface area by using just compass and straight edge.
3. Creating a circle and a square with equal perimeters by using just compass and straight edge.
4. Creating an Equilateral triangle and a circle with equal perimeters by using just compass and straight edge.
5. Creating an Equilateral triangle and a circle with he same surface area by using just compass and straight edge.
6. Creating a Pentagon and a circle with equal perimeters by using just compass and straight edge.
7. Creating a Pentagon and a circle with the same surface area by using just compass and straight edge.
8. Creating a Cube and a sphere with the same surface area by using just compass and straight edge.
9. Creating a Cube and sphere with the same volume.
10.Creating a Phi Pyramid and a sphere with the same surface area by using just compass and straight edge.
11.Creating a Phi Pyramid and a sphere with the same volume.
12. Creating a Locun ratio Pyramid and a sphere with the same surface area by using just compass and straight edge.
13. Creating a Locun ratio Pyramid and a sphere with the same volume.
Explaining the causes of the Quadrature of the circle part 1:
First regarding the creation of a circle and a square with equal perimeters meaning the circumference of the circle is equal in measure to the perimeter of the square, the width of the square must be equal to 1 quarter of the circle’s circumference resulting in the perimeter of the square being the same measure as the circumference of the circle. For example if the circumference of the circle is 8 then the edge of the square with a perimeter that is equal to a circle with a circumference of 8 must be 2.
Also if the square and circle share the same center and the circumference of the circle is equal to the perimeter of the square then the radius of the circle must be the longer measure of a 1.272019649514069 ratio rectangle while half the central width of the square must be the shorter measure of a 1.272019649514069 ratio rectangle.
If a circle and square are created with the perimeter of the square being the same measure as the circumference of the circle and the circle and square do NOT share the same center then the diameter of the circle CAN be the longer measure of a 1.272019649514069 ratio rectangle while the edge of the square CAN be the shorter measure of a 1.272019649514069 ratio rectangle but this is NOT compulsory.
In another example the edge of the square is the longer measure of a 1.272019649514069 ratio rectangle while the shorter measure of the 1.272019649514069 ratio rectangle is equal in measure to 1 quarter of the real value of Pi = 3.144605511029693.
Second regarding the creation of a circle and a square with equal areas the radius of the circle must be the longer measure of a 1.127838485561682 ratio rectangle while half the central width of the square must the shorter measure of a 1.127838485561682 ratio rectangle if the circle and square share the same center. If the circle and square do NOT share the same center and the circle and square have the same surface area then the diameter of the circle CAN be the longer measure of 1.127838485561682 ratio rectangle while the edge of the square CAN be the shorter measure of a 1.12783848556 ratio rectangle but this is NOT compulsory.
The relationship between the circle and the square having the same perimeter or the same area is a result of 2 ratios that are related to the Golden ratio of cosine (36 degrees) multiplied by 2 = 1.618033988749895 being used and those 2 ratios again are:
• The square root of the Golden ratio also called the Golden root = 1.272019649514069.
The Golden root 1.272019649514069 is the result of either the diameter of a circle being divided by 1 quarter of a circle’s circumference or the radius of a circle being divided by one 8th of a circle’s circumference.
The square root of the Golden ratio = 1.272019649514069 also applies to the perimeter of a square divided by the circumference of a circle with a diameter equal to the width of the square. The square root of the Golden ratio = 1.272019649514069 also applies to the surface area of a square divided by the surface area of a circle with a diameter equal to the width of the square.
The square root of the Golden ratio = 1.272019649514069 also applies to the surface area of a square divided by the surface area of a circle with a circumference equal in measure to the perimeter of the square.
The second longest edge length of a Kepler right triangle divided by the shortest edge length of a Kepler right triangle is the square root of the Golden ratio also called the Golden root = 1.272019649514069. The hypotenuse of a Kepler right triangle divided by the second longest edge length of a Kepler right triangle is the square root of the Golden ratio = 1.272019649514069.
The square root of the Golden ratio = 1.272019649514069 can also be gained if the surface area of circle is multiplied by 16 and then the result of the surface area of a circle being multiplied by 16 is then divided by the circumference of the circle squared. If the measure for the diameter of a circle is multiplied by 4 and the result of multiplying the measure of a circle’s diameter by 4 is divided by the measure for the circumference of a circle the result is also the square root of the Golden ratio also called the Golden root = 1.272019649514069.
4 divided by Golden Pi = 3.144605511029693 = the square root of the Golden ratio = 1.272019649514069.The square root of the Golden ratio = 1.272019649514069 also applies to the calculation of the surface area of a circle when the surface area of a square with a width that is equal to 1 quarter of the circle’s circumference is multiplied by the square root of the Golden ratio = 1.272019649514069. If the surface area of a circle is multiplied by the square root of the Golden ratio = 1.272019649514069 the result is the square root for the diameter of the circle.
• The square root of the Golden root = 1.127838485561682.
The square root of the Golden root 1.127838485561682 can be gained if the diameter of a circle that has the same surface area as a square is divided by the width of the square that has the same surface area as the circle. The square root of the Golden root 1.127838485561682 can also be gained if the radius of a circle that has the same surface area as a square is divided by half the width of the square that has the same surface area as the circle.
The square root of the Golden root 1.127838485561682 can also be gained if a circle and a square with the same surface area are created and the perimeter of the square is divided by the circumference of the circle. The second longest edge length of a Illumien right triangle divided by the shortest edge length of a Illumien right triangle is the ratio The square root of the Golden root = 1.127838485561682.
If a circle and a square are created with equal areas of measure and the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 quarter of the circle’s circumference that has the same surface area as the square and if 1 quarter of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the diameter of the circle.
If the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the diameter of the circle with the same surface area as the square.
If a circle and a square are created with equal areas of measure and half the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 eighth of the circle’s circumference that has the same surface area as the square and if 1 eighth of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the radius of the circle.
If half the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the radius of the circle with the same surface area as the square.
If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the radius or the diameter of a circle that has the same surface area to the already existing square that already has a circle with a circumference that is equal to the perimeter of the square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for the radius or diameter of the circle that has the same surface area to the already existing square that has a perimeter that is equal in measure to the circumference of the already existing circle.
Alternatively If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the edge of a square that has the same surface area as the already existing circle that has a circumference equal in measure to the perimeter of the already existing square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the already existing square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for half the edge of the square or the edge of the square that has the same surface area as the already existing circle that has a circumference that is equal in measure to the perimeter of the already existing square.
“How to create a circle and a square with the same surface area by using compass and straight edge part 1”.
A Kepler right triangle is half of a square root of the Golden ratio = 1.272019649514069 rectangle.
The mean proportional of a rectangle is the square root for the surface area of a rectangle.
The surface area of a rectangle can be calculated if the shorter edge of the rectangle is multiplied by the longer edge of the rectangle.
The mean proportional of a square root of the Golden ratio = 1.272019649514069 rectangle is the same measure as the diameter of a circle with the same surface area as the square that is located on the shorter edge of the square root of the Golden ratio = 1.272019649514069 rectangle.
The mean proportional of a rectangle that has its longer edge equal to the shortest edge length of a Kepler right triangle while the shorter edge of the rectangle is equal to 1 quarter of the second longest edge length of the Kepler right triangle is equal to the radius of a circle that has the same surface area as the square that us located on the shortest edge length of the Kepler right triangle.
The construction process of a circle and a square with the same surface area:
Construct a Kepler right triangle because the second longest edge length of a Kepler right triangle is the longer edge of a square root of the Golden ratio = 1.272019649514069 rectangle, while the shortest edge of the Kepler right triangle is the shorter edge of the square root of the Golden ratio = 1.272019649514069 rectangle and the hypotenuse of the Kepler right triangle is the diagonol of the square root of the Golden ratio = 1.272019649514069 rectangle.
A Kepler right triangle is half of a square root of the Golden ratio = 1.272019649514069 rectangle.
The mean proportional of a rectangle is the square root for the surface area of a rectangle.
The surface area of a rectangle can be calculated if the shorter edge of the rectangle is multiplied by the longer edge of the rectangle.
If an individual can construct a Kepler right triangle by using compass and straight edge then that individual can square the circle. We do NOT need to know anything about Pi to create a circle and a square with the same surface area. We must learn about the Golden ratio = Cosine (36 degrees) multiplied by 2 = 1.618033988749895 and the square root of the Golden ratio = 1.272019649514069 and also the square root of the square root of the Golden ratio = 1.127838485561682 if we want to create a circle and a square with the same surface area.
If a circle and a square are created with equal areas of measure and the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 quarter of the circle’s circumference that has the same surface area as the square and if 1 quarter of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the diameter of the circle.
If the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the diameter of the circle with the same surface area as the square.
If a circle and a square are created with equal areas of measure and half the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 eighth of the circle’s circumference that has the same surface area as the square and if 1 eighth of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the radius of the circle.
If half the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the radius of the circle with the same surface area as the square.
If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the radius or the diameter of a circle that has the same surface area to the already existing square that already has a circle with a circumference that is equal to the perimeter of the square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for the radius or diameter of the circle that has the same surface area to the already existing square that has a perimeter that is equal in measure to the circumference of the already existing circle.
Alternatively If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the edge of a square that has the same surface area as the already existing circle that has a circumference equal in measure to the perimeter of the already existing square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the already existing square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for half the edge of the square or the edge of the square that has the same surface area as the already existing circle that has a circumference that is equal in measure to the perimeter of the already existing square.
2 divided by the square root of Golden Pi = 1.773303558624324 = 1.127838485561682.
Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36 degrees) multiplied by 2 = 1.618033988749895.
Hmm
❤
I have construct square root pi ...
Any ratio that is not the result of a circle's circumference divided by a circle's diameter is not pi and that should be easy for you to understand.
Your value of Pi = 3.141592653589793 is wrong because it has not been derived from dividing the circumference of a circle by the diameter of a circle, instead your value of pi was originally derived from Archimedes’ multiple polygon limit calculus approach that involves constructing circles around polygons and also constructing circles inside of polygons.
Constructing circles inside of polygons and also constructing circle's around polygons is not the same as circumference of circle divided by diameter of circle.
It is impossible for a polygon to become a circle and that means that it does not matter how many edges that a polygon has there will forever be a gap between the edge of the polygon and the curvature of the circle that contains the polygon.
A circle does not have any edges.
It is impossible for a polygon with an infinite amount of edges to exist because a polygon is known and identified by the amount of edges that a polygon has for example a decagon is a polygon that is known to have 10 edges.
Archimedes’ multiple polygon calculus limit approach to finding pi can only produce approximations for Pi but never produce the real value of Pi.
Using calculus to discover Pi is a waste of time and effort because there will forever be an area under the curvature of a circle because the curvature of space is fractal in nature. The more area under a curve is magnified the more crevices can become visible.
Academic mathematicians of today are now using computer simulations based on a infinite series of numbers that they assume will just magically result in the correct value of Pi but the problem with infinite series is how can anybody use a random series of numbers to converge to Pi when they have not discovered Pi due to the fact that they have never divided the circumference of a circle by the diameter of a circle in their entire lives ?
Infinite series is not the same as circumference of circle divided by diameter of circle and that means that anybody that is using infinite series to find Pi is either knowingly or unknowingly an idiot.
Pi means circumference of circle divided by diameter of circle.
I am here to stop mathematicians from committing fraud.
If you do not understand that any ratio that is not derived from a circle's circumference divided by a circle's diameter is not Pi then you are confused.
You are committing fraud by ignoring that fact and I cannot tolerate that.
You must divide the circumference of a circle by the diameter of a circle to discover Pi or alternatively divide the surface area of a circle by the surface area of the square that is located on the radius of the circle.
You can divide the circumference of a circle into almost any number or ratio using compass and straight edge and that is so easy to do.
Compute the measure for the diameter of the circle by using the diameter of the circle as the edge of a right triangle.
I must repeat: any ratio that is not the result of a circle's circumference divided by a circle's diameter is not Pi and if you still do not understand that then you are an idiot.
Common sense should tell you that to get pi you must divide the circumference of a circle by the diameter of a circle because the dictionary says that Pi is the ratio of a circle's circumference divided by a circle's diameter.
The dictionary says that Pi is the ratio of a circle's circumference divided by a circle's diameter.
There are only 2 ways to discover Pi and that is to divide the circumference of a circle by the diameter of a circle or alternatively divide the surface area of a circle by the surface area of the square that is located on the radius of the circle. Anything other than circumference of circle divided by diameter of circle or surface area of circle divided by the surface area of the square that is located on the radius of the circle is not Pi.
If you are not dividing the circumference of a circle by the diameter of a circle or dividing the surface area of a circle by the surface area of the square that is located on the radius of the circle then you cannot honestly discover Pi and if you claim to have discovered Pi while refusing to divide the circumference of a circle by the diameter of a circle or divide the surface area of a circle by the surface area of the square that is located on the radius of the circle then you are a fraud because the only 2 ways to discover Pi is to divide the circumference of a circle by the diameter of a circle or divide the surface area of a circle by the surface area of the square that is located on the radius of the circle.
lol