Thanks for pointing out the proposition from Euclid. I have my own copy of Heath's Volume II, books III-IX.

Im personally really interested in history of mathematics (im sure im not alone) ,so this topic is perfect! More topics on history of mathematics please! :)

@ciaranmcevoy9875

3 жыл бұрын

That's great to hear pal! I'll most certainly be doing more videos on the history of maths.

Great video

Hi Ciaran, I like your videos very much! Thank you for spending the time to put them together. I would like to ask you a question about how to introduce pi to young learners. They learn that "Pi is irrational and pi is Circumference/diameter". For the definition not to contradict itself, either circumference or radius must be irrational. The circumference and diameter are finite, they start and end. So, question: How can something finite be represented by a number that has infinitely many decimal places? I know that there are some explanations to this phenomenon but I am interested to hear how you would explain it. Please keep making videos! They're very engaging and meaningful! Cheers:)

@ciaranmcevoy9875

2 жыл бұрын

Wow Gulnur, thank you very much! And what a fabulous question! I'm training to be a maths teacher at moment and that, without doubt, will be something I'd like to think about. I would love to make a video on that, thanks for the spark of inspiration.

@ffggddss

2 жыл бұрын

There's no reason that a finite number (in size) can't have a decimal representation that's infinite. You could, after all, ask the same question about ⅓, or ¹/₇ , each of which also has infinitely many decimal digits. But I gather that your concern is that infinitely many decimal digits represents an infinite sum, and that IS something of a puzzle - the ancients knew the concept as Zeno's Paradox. If you look that up (I'd suggest a Wikipedia search for starters), you should be able to find a better explanation than I could give here without a monstrously lengthy post (tl;dr). Fred

11:03 Archimedes must have had tremendous thirst for knowledge.

@ciaranmcevoy9875

4 ай бұрын

Absolutely!

Thank u for clarity to a great extent. Deserve praise for your not mentioning even fractional numbet.. many were guessing how he calculated value of root over 3, India's s Baudhyan on sulvasutra formulated value of root over 2 in 800 be , following it, oondcan easily find out 1351/ 780. But other value ,it was difficult. Some conjectured p^2- 3x^2= 1. And -2, . Indeterminate second degree equation. Brahmagupta detailed I. Vargs Prakrit p^2 - n x^2 =1, . It was integer solution. In Diaohantine , this wS rational solution. However, want to know, how Archimedes calculated 265/ 153 for root over 3.requsr yo If u make calculations for every steps. Namaksr from India.

@kantaprasadsinha8025

2 жыл бұрын

Read decimal fraction number.

2:55

Mr MCEVOY do you have someone called Timmy in your class?

@Fandom_wanderer

Жыл бұрын

Are u in his clash

@willX25

Жыл бұрын

@@Fandom_wanderer i am😎😎😎

@Fandom_wanderer

Жыл бұрын

@@willX25 I’m Timmy and mate

More information saying that traditional Pi = 3.141592653589793 is false part 1 - kloka: The currently accepted value of Pi = (10 ^ 12)/(16255123/10213395)/(2)/(10 ^ 11) = 3.141592653589793 and is called regular Pi by some mathematicians. Regular Pi = (10 ^ 12)/(16255123/10213395)/(2)/(10 ^ 11) = 3.141592653589793 is wrong and does NOT belong to a circle but belongs to a polygon with many edges instead and you MUST always remember that a circle does NOT have any edges so that further proves that Traditional Pi = (10 ^ 12)/(16255123/10213395)/(2)/(10 ^ 11) = 3.141592653589793 is false. Traditional Π = Pi = 51066975/16255123 = 3.141592653589793 is false. Traditional Pi = ((10 ^ 42)/(30685681/9640191)) = 3.141592653589793 is false. Traditional Pi = (4/√(48908982/30169519)) = 3.141592653589793 is false. Common sense should tell you that a polygon and a circle are NOT the same thing but you are acting as if a circle and a polygon are the same thing when a circle is different from a polygon. A circle is defined by my dictionary as a plane figure with points that are equally distant from a central point. My dictionary says that a polygon is a plane figure with a minimum of 3 edges. A polygon can have many edges. It is impossible for a polygon to become a circle and that means that Pi MUST be larger than 3.141. 3.141 belongs to a polygon with more than a trillion edges but a circle does NOT have any edges. A polygon is identified and known by the number of edges that the polygon has got for example a Decagon is a polygon with 10 edges. It is impossible for a polygon with an infinite amount of edges to exist because a polygon is identified and known by a limited amount of edges. I repeat a circle does NOT have any edges. There will forever be a gap between the edge of the polygon and the curvature of the circle that contains the polygon it does NOT matter if the polygon has 10 ^ 98 edges because the gap between the edge of the polygon and the curvature of the circle that contains the polygon will forever remain. There can only be 1 Pi and that Pi MUST full-fill the following criteria: 1. That Pi MUST fit the definition of Pi from the dictionary the ratio of a circle's circumference divided by a circle's diameter. 2. That value of Pi Must have a physical counterpart. So that means the real value of Pi cannot be transcendental because transcendental numbers do NOT exist in the real world period. Transcendental numbers are only found on calculators. 3. There must be more than 1 geometric proof for the true value of Pi including the squaring of the circle and that involves both the creation of a circle that has a circumference that is the same measure as the perimeter of a square with just the aid of compass and straight edge alone and also the creation of a circle and a square with the same surface area with just the aid of compass and straight edge alone. Only Golden Pi = 4/√φ = 3.144605511029693144 can be used to square a circle with just compass and straight edge alone. To calculate Pi accurately get a piece of foam board that is larger than A0 such as 2A0 and create upon the surface of the foam board that is larger than A0 such as 2A0 a circle with 1-meter diameter by using a beam compass with a radius of 50 centimeters. After the circle with a 1-meter diameter has been created upon the flat surface of the piece of foam board that is larger than A0 such as 2A0 use a Rotary circle cutter with a metal blade and a radius of also 50 centimeters to cut around the contours of the circumference of the circle with a 1-meter diameter that was created upon the flat surface of the foam board that is larger than A0 such as 2A0. The length of the tape measure should be a minimum of 3200 millimeters. Wrap the length of the tape measure around the contours of the circumference of the circle with a 1-meter diameter that was created upon the piece of foam board that is larger than A0 such as 2A0. Make sure that the measurements are facing towards your eyes by measuring inwards around the circumference of the circle. The measurement should go all around the circumference of the circle finishing back at the starting position. The diameter of the circle MUST be equal to a minimum of 1-meter = 1000 millimeters or 100 centimeters. Do NOT use a circle with a diameter that is smaller than 1-meter. If the diameter of the circle is reduced to 1 then the circumference of the circle is Pi. Count the amount of times the diameter of the circle fits around the circumference of the circle and then divide the measure for the circumference of the circle by the diameter of the circle to discover the true value of Pi = 3.1446. If the diameter of a circle is 1-meter = 1000 millimeters then the circumference of the circle has a measure of 3144.6 millimeters. 3144.6 divided by 1000 = 3.1446. 4 divided by 3.1446 = the ratio 1.272021878776315. The ratio 1.272021878776315 is an approximation of the square root of the Golden ratio = √φ = 1.272019649514069 because if the ratio 1.272021878776315 is squared the result is the ratio 1.618039660085626. The ratio 1.618039660085626 is an approximation of the Golden ratio = (√(5) plus 1)/2 = (φ) = 1.618033988749895. The ratio 1.618039660085626 squared = the ratio 2.618052341610009. The Golden ratio = (φ) = 1.618033988749895 squared = (√(5) plus 3)/2 = 2.618033988749895. Proof that the Kepler right triangle is the key to the true value of Pi can also be demonstrated if the length of the measuring tape is a minimum of 4 meters = 4000 millimeters, because if the circumference of the 1-meter diameter circle = 3144.6 millimeters is marked and placed on a horizontal straight line while the 1-meter diameter of the circle = 1000 millimeters is multiplied 4 equal times on a vertical straight line the result is the circumference of the 1-meter diameter circle = 3144.6 millimeters is the shortest edge length of a Kepler right triangle while the multiplication of the 1-meter diameter of the circle = 1000 millimeters = 4000 millimeters is the second longest edge length of a Kepler right triangle. The multiplication of the 1-meter diameter of the circle = 1000 millimeters by 4 equal parts is 4000 millimeters. 4000 divided by 3144.6 = the ratio 1.2720218787763. The ratio 1.2720218787763 is an approximation of the square root of the golden ratio of √φ = 1.272019649514069, because the ratio 1.2720218787763 squared meaning that the ratio 1.2720218787763 times the ratio 1.2720218787763 = the ratio 1.6180396600856. Apply the Pythagorean theorem to the 2 right angles that are created from the results of the diameter of the circle being multiplied 4 equal times upon a vertical straight line while the circumference of the circle is placed upon a horizontal straight line, to get the hypotenuse of a Kepler right triangle. We can find the correct decimal expansion for Pi as 4/√φ = 3.144605511029693144 and that is to 18 decimal places. We can have as many decimal places for Pi that are larger than 18 as long as we remember that the exact value for Pi = 4/√φ = 3.144605511029693144.

More information saying that traditional Pi = 3.141592653589793 is false part 2 - kloka: Pi is also defined as the ratio of the area of a circle divided by the area of the square that is located on the radius of the circle. If a circle is created with a diameter that is the same measure as the longer edge length of a Square root of the golden ratio √φ = 1.272019649514069 rectangle then one-quarter of the circle’s circumference is the same measure as the shorter edge length of a Square root of the golden ratio √φ = 1.272019649514069 rectangle, plus both the surface area of the circle and the surface area of the Square root of the golden ratio √φ = 1.272019649514069 rectangle have the same surface area. A Square root of the golden ratio √φ = 1.272019649514069 rectangle can be divided into 8 Kepler right triangles and if the shortest edge length of a Kepler right triangle is reduced to 1 then the hypotenuse is equal to the Golden ratio of cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895, while the second longest edge length of the Kepler right triangle is equal to the Square root of the golden ratio √φ = 1.272019649514069, according to the Pythagorean theorem. A Square root of the golden ratio √φ = 1.272019649514069 rectangle that has been divided into 8 Kepler right triangles has a surface area equal to 4 times √φ = 5.088078598056276. A circle with a diameter that is equal to the longer edge length of a Square root of the golden ratio √φ = 1.272019649514069 rectangle that has been divided into 8 Kepler right triangles also has a surface area equal to 4 times √φ = 5.088078598056276. The longer edge length of the Square root of the golden ratio √φ = 1.272019649514069 rectangle that has been divided into 8 Kepler right triangles has a surface area equal to 4 times √φ = 5.088078598056276 is also equal to 2 times √φ = 2.544039299028138. The shorter edge length of the Square root of the golden ratio √φ = 1.272019649514069 rectangle that has been divided into 8 Kepler right triangles has a surface area equal to 4 times √φ = 5.088078598056276 is also equal to 2. A circle with a diameter that is equal to the longer edge length of a Square root of the golden ratio √φ = 1.272019649514069 rectangle that has been divided into 8 Kepler right triangles also has a radius that is equal to the Square root of the golden ratio √φ = 1.272019649514069. √φ times √φ = the Golden ratio of cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895. Circumference of the circle = 8. 1-quarter of the circle’s circumference = 2. Diameter of the circle = 2 times √φ = 2.544039299028138. Radius of the circle = the Square root of the golden ratio √φ = 1.272019649514069. The surface area of the circle divided the surface area of the square that is located on the radius of the circle = 4/√φ = 3.144605511029693144, because 4/√φ times √φ times √φ = 4 times √φ/((φ)) = 4/√φ = 3.144605511029693144. Surface area of the circle = 4/√φ times √φ times √φ = 4 times √φ = 5.088078598056276. Radius of the circle = the Square root of the golden ratio √φ = 1.272019649514069. Radius of the circle squared = √φ times √φ = the Golden ratio of cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895. Pi is also defined as the surface area of the circle divided the surface area of the square that is located on the radius of the circle.

My math teacher looks just like you

@willX25

Жыл бұрын

My maths teacher is called mrmcevoy aswell 😂

@willX25

Жыл бұрын

And he looks a lot like you aswell ciaran!

@Fandom_wanderer

Жыл бұрын

@@willX25 I have a friend called Will Smith what a coincidence 😆😆😆😆

@gojoXroman

Жыл бұрын

I have a friend called will smith too 😮😂

@willX25

Жыл бұрын

@@Fandom_wanderer wait do I know u?

how come the ratio of OA to AC is equal the ratio of square root of three? (4:00) How did Archimedes know that root was right? OK, I did a research and it can be proven by Pythagoras theorem that this length is the square root of three. But it is a gap for my taste in the video.

@ciaranmcevoy9875

2 жыл бұрын

I appreciate the feedback and interest Bernat. And yes, I had the same train of thought as you, and I found multiple papers and sources discussing how the Greeks and Egyptians calculated square roots. I decided that this is most certainly a video in itself as it's always fascinated me how they did it at all, so eventually I'll plan a video for that.

@kantaprasadsinha8025

2 жыл бұрын

Value of root over 3 for 1351/780 done by Baudhysna principle ( 800 bce in India). But 265/153 you have to recourse to x^2 - 3y^= -2,

so they were stupid to have to calculate things, so sad

@Jkauppa

2 жыл бұрын

you dont have enough if you have to calculate, ration, pun intended

@Jkauppa

2 жыл бұрын

hard to listen, s-lackers

@Jkauppa

2 жыл бұрын

hand calculated piece-wise line-integral, multiplicates of the line segments, any function, circle y=sqrt(1-x^2), from the x^2+y^2=1 equation of circle

@Jkauppa

2 жыл бұрын

dont have to obey the rule

@Jkauppa

2 жыл бұрын

inscribed circle multicon, polygon, as the minimum, of the solution, greater than solution, that is as close as that many line segments can approximate the function shape, like area piece-wise sum approximation by a flat line through the center of the w/n wide segment, but same for line or circumference of the shape, function, circle, ellipse, any

The traditional value of Pi = 3.141592653589793 is wrong and dangerous 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 any mathematician to understand. The traditional 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 the traditional value of pi = 3.141592653589793 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 circles 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 a circle is fractal in nature. The more the 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 an individual does not understand that any ratio that is not derived from a circle's circumference divided by a circle's diameter is not Pi then that individual is confused. Academic Mathematicians are committing fraud by claiming that the ratio 3.141592653589793 is the correct value of Pi. It is wrong for Academic mathematicians to claim that Pi MUST be transcendental and Squaring the circle is impossible when the fact remains that mathematicians do NOT know what the correct value for Pi is because Academic mathematicians are only using an approximation of Pi due to their refusal to measure a circle with a diameter of 1-meter and count the amount of times the 1-meter diameter fits around the curvature of the circle. To discover the correct value of Pi the circumference of a circle MUST be divived 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. The correct value for pi is 4/√φ = 3.1446055110296931442782343433718357180924882313508929506596078804 The correct value for pi is 4/√φ = 3.1446055110296931442782343433718357180924882313508929506596078804... The correct value for pi = 4/√φ = 3.144605511029693144 is NOT transcendental because of the following minimal polynomial that is associated with it: x^4 + 16 x^2 - 256 The correct value for pi can be confirmed by creating a circle with a diameter of 1-meter upon a piece of foam board that is larger than A0 such as 2A0 with a beam compass with a radius of 50 centimeters and also a rotary circle cutter with a radius of 50 centimeters. A 4 meter tape measure can be used to measure the amount of times the diameter of 1-meter fits around the curvature of the circle to determine the circumference of the circle, so that the circumference of the circle circle can be divided by the diameter of the circle with 1-meter to discover the true value of pi. Experiments involving physical measurement of a circle with a diameter of 1-meter have confirmed that the correct value of pi is a minimum of 3.1446 and is larger than the assumed value of pi = 3.1415. The decimal expansion for pi is infinite and to discover the decimal expansion for pi beyond 3.1446 4 MUST be divided by 3.1446. 4 divided by 3.1446 = the ratio 1.2720218787763. 4 divided by the ratio 1.2720218787763 = 3.1446. The ratio 1.2720218787763 is an approximation of the square root of the golden ratio of √φ = 1.272019649514069, because the ratio 1.2720218787763 squared meaning that the ratio 1.2720218787763 times the ratio 1.2720218787763 = the ratio 1.6180396600856. Proof that the Kepler right triangle is the key to the true value of Pi can also be demonstrated if the length of the measuring tape is a minimum of 4 meters = 4000 millimeters, because if the circumference of the 1-meter diameter circle = 3144.6 millimeters is marked and placed on a horizontal straight line while the 1-meter diameter of the circle = 1000 millimeters is multiplied 4 equal times on a vertical straight line the result is the circumference of the 1-meter diameter circle = 3144.6 millimeters is the shortest edge length of a Kepler right triangle while the multiplication of the 1-meter diameter of the circle = 1000 millimeters = 4000 millimeters is the second longest edge length of a Kepler right triangle. The multiplication of the 1-meter diameter of the circle = 1000 millimeters by 4 equal parts is 4000 millimeters. 4000 divided by 3144.6 = the ratio 1.2720218787763. The ratio 1.2720218787763 is an approximation of the square root of the golden ratio of √φ = 1.272019649514069, because the ratio 1.2720218787763 squared meaning that the ratio 1.2720218787763 times the ratio 1.2720218787763 = the ratio 1.6180396600856. The ratio 1.6180396600856 is an approximation of the golden ratio of the square root of 5 plus 1 divided by 2 = (φ) = 1.61803398874895. It is evident that the infinite decimal expansion for the correct value of pi can be derived from the formula 4 divided by the square root of the golden ratio = 4/√φ = 3.144605511029693144.. Apply the Pythagorean theorem to the 2 right angles that are created from the results of the diameter of the circle being multiplied 4 equal times upon a vertical straight line while the circumference of the circle is placed upon a horizontal straight line, to get the hypotenuse of a Kepler right triangle. A wooden circle with a diameter of 1-meter has also been measured and used to confirm that the correct value of pi is 4/√φ = 3.1446. Below are videos involving the measurement of circles with a diameter of 1-meter to prove that the correct value of pi = 4/√φ = 3.144605511029693144: I must repeat: any ratio that is not the result of a circle's circumference divided by a circle's diameter is not Pi. Introduction to the true value of Pi = 4/√φ = 3.144605511029693144 - Pi intro video brand: m.kzread.info/dash/bejne/Y3iV2a-KYa-8ZrQ.html Proof 7 Part 1 Pi Circumf Measurement: m.kzread.info/dash/bejne/mHWIzquzmNedhqw.html Pi tape foam board circle 1: m.kzread.info/dash/bejne/fXp72dlpqpmugto.html Pi Tape Measurement Foam Board Circle 2: m.kzread.info/dash/bejne/fYh-1aWzeK_ZddI.html Pi Tape Measurement Foam Board Circle 3: m.kzread.info/dash/bejne/l5yeo7Cdgs_RpNo.html Pi tape measurement Hardwood : m.kzread.info/dash/bejne/dod1rZiRk8e8paw.html Pi video Math brand: m.kzread.info/dash/bejne/oKqew5qrd6bIqrw.html Geo Proof 1 Brand: m.kzread.info/dash/bejne/eHZ_zphrXZSZg7Q.html Geo Proof 2 Brand: m.kzread.info/dash/bejne/d2V_t7V-ltWaZs4.html Geo Proof 4 Brand: m.kzread.info/dash/bejne/lmZmy7Z-fqutp7g.html Geo Proof 6 Brand: m.kzread.info/dash/bejne/iIqrrJaDZNO7drQ.html 5 More Constants Brand: m.kzread.info/dash/bejne/dI2gp9iSls-1oNY.html Fixing and Correcting the problems caused by using traditional Pi: kzread.info/dash/bejne/imWOo9anZsqThso.html Harry Lear Interview Apophis & Pi: m.kzread.info/dash/bejne/g3-N2s2YldOqqrQ.html www.measuringpisquaringphi.com PYTHAGOREAN THEOREM: en.wikipedia.org/wiki/Pythagorean_theorem Golden ratio: en.wikipedia.org/wiki/Golden_ratio Back to basics: How to measure a circle article about Pi: www.thunderbolts.info/forum3/phpBB3/viewtopic.php?f=11&t=341