This video deserves way more views. Ever thought about designing a ballista with vertical arm? Been wanting to make one

This is great. It didn't fully click when watching other videos. I understood how it works, but I didn't understand why was it created in the first place and its application.

I was expecting an argument about the homomorphism between the real multiplicative and additive group

I lole yhat you gave burghi due credit...the meeting of napier and briggs is a classic demonstration of the scientific method at work, in spirit and indeed

Logarithms: do they even exist?

I have one doubt for a long time can you give the answer for it. Log 100 value is 2 we can write 10*10 like wise log 1000 value is 3 we can write it a 10*10*10 all of it give some meaning then if we get log value in fraction eg: log 45 value is 1.6532 how we can write it as multiple of 10.......10*?. plz don't ignore the mail I literally waiting for reply

I am not a mathematician. I am just a self taught software developer who is struggling though a computer science course. One concept I keep running into is logarithms. Finding information on how to use them has been straightforward, but felt like only half the story. I wanted to know why they were even a concept. I knew they were useful, but I did not know what problem it was meant to solve. It felt like they only existed just for the sake of being esoteric so problems could be solved in a specific way. To my mind they were a solution searching for a problem. It just felt like an alternate way to write exponential equations. Your video does a wonderful job at starting to help me understand they are indeed vital to understand and not needlessly esoteric at all. Thank you!

❤️👏🏻

Slight problem in that epidemics have been known not to grow exponentially since, at least, Farr's Law of 1840. They have logistic growth as per the standard SIR model of 1927 as you full well know.

woww excellent content brother 🙇

website not available?

Could have used some examples of how log helped the mathematicians.

In school we used log and antilog tables without ever being made aware of the principle behind them. Perhaps it was but we (or maybe I) were/was too young and naturally ignorant to grasp the harder part, this essential cleverness from back hundreds of years earlier. I like mathematics much more many, many decades later having re-learned much of it out of residual curiosity. With a better insight I could have loved it way back then instead of just enduring the robotic procedures like grinding through some hated language. Just entering the teenage years of course carried the handicap of emerging laziness and arrogance, the best years and the worst for learning?

Great video!

I think you've done a fine job with this. Napier's logarithms and Harrison's clocks are two British ideas that made marine navigation much easier and saved countless lives at sea.

What is 3x3 dertminate and why its use

Because you need another inverse for exponentiation since it's not "symmetrical" anymore when you get to this tier

This is a very nice explanation! Are you planning on making more videos in the future?

I still use exponentials to calculate how long it takes for my coffee to cool down.

00:36 I dont think bro was joking

Because its not in focus, the device on the shelf looks like a blackening banana on a stand.

love ur sense of humour

This is an excellent explanation of why matrices even exist. We home school, and we just started learning matrices in algebra. My son was very frustrated and asked, "Why do these even exist?" Thank you for answering his question.

Log is used nearly everywhere in number theory as, due to be very nature of how base systems work. The number of digits a number has is very very intrinsically tied to its logarithm in that case.

Why on earth would logarithms be disliked? There's nothing to them; I've always thought of them as every bit as much "bread and butter" math as arithmetic.

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.kzbin.info/www/bejne/Z3XEqICHZrGJbLM Proof 7 Part 1 Pi Circumf Measurement: m.kzbin.info/www/bejne/nHK3nXywndlqjKs Pi tape foam board circle 1: m.kzbin.info/www/bejne/gXeqqKpmr5t7iNk Pi Tape Measurement Foam Board Circle 2: m.kzbin.info/www/bejne/gYWtpHawfbGme9E Pi Tape Measurement Foam Board Circle 3: m.kzbin.info/www/bejne/m5nNcoGah9Geqtk Pi tape measurement Hardwood : m.kzbin.info/www/bejne/eoSkfGmOmMmJq6s Pi video Math brand: m.kzbin.info/www/bejne/pKfNkmuofKiVsLs Geo Proof 1 Brand: m.kzbin.info/www/bejne/fHOunWloYpZmibM Geo Proof 2 Brand: m.kzbin.info/www/bejne/e2KuhoZ7m9dnbM0 Geo Proof 4 Brand: m.kzbin.info/www/bejne/mmOVmod7g616rbc Geo Proof 6 Brand: m.kzbin.info/www/bejne/jIfae2eAadWIfLM 5 More Constants Brand: m.kzbin.info/www/bejne/eIrPdqmPm9GCptU Fixing and Correcting the problems caused by using traditional Pi: kzbin.info/www/bejne/jmK9cqeka8xgjMk Harry Lear Interview Apophis & Pi: m.kzbin.info/www/bejne/h3y8qZ6VmtV3sLM 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

More information saying that traditional Pi = 3.141592653589793 is false part 3 - kloka: Any circle can be squared by using just compass and straight edge alone when using the real value of Pi = 4/√φ = 3.144605511029693144. After you have measured a circle with a 1 meter diameter to find the exact value of Pi for yourself the next stage is to square the circle to further prove that 4/√φ = 3.144605511029693144 is the real and true value for Pi. If you have a given circle and you want to create a square with a perimeter that has the same measure as the curvature of the circle then just use your calculator and divide the diameter of the circle by the square root of the Golden ratio = √φ = 1.272019649514069 and you will automatically have the width of a square that has a perimeter with the same exact measure as the curvature of the circle. Multiply Pi = 4/√φ = 3.144605511029693144 times the diameter of the circle to confirm that the circumference of the circle is the same exact measure as the perimeter of the square. To get the second quadrature of the circle just use the square root of the square root of the Golden ratio = √√φ = 1.127838485561682 by dividing the diameter of given circle to get the width of a square with the same surface area as the given circle. Please remember that the ratio √√φ = 1.127838485561682 is the square root of the ratio √φ = 1.272019649514069 and the ratio √φ = 1.272019649514069 is the square root of the Golden ratio of cosine (36 degrees) multiplied by 2 = (φ) = (√(5) plus 1)/2 = 1.618033988749895. The real value of pi is NOT transcendental because the real value of Pi = 4/√φ = 3.144605511029693144 is the only value of pi that can fit the following polynomial equation: 4th dimensional equation/polynomial for Golden Pi = 4/√φ = 3.144605511029693144 Minimal polynomial: x4 + 16x2 - 256 = 0. www.tiger-algebra.com/drill/x~4-16x~2-256=0/ The real value of Pi = 4/√φ = 3.144605511029693144: Please copy and paste the following link into your web browser if you cannot click onto the following link: www.wolframalpha.com/input/?i=4+divided+by+the+square+root+of+the+golden+ratio Please click on the red dots in the following link to confirm that the real value of Pi = 4/√φ = 3.1446 is not transcendental. The real value of pi = 4/√φ = 3.144605511029693144. Minimal polynomial: x4 + 16x2 - 256 = 0 www.wolframalpha.com/input/?i=x4+%2b+16x2+%e2%80%93+256+%3d+0

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.

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.

Hello mr mcevoy, you taught me last year best teacher ever

Blew my mind!

I am engineering student from india and I really like your reasearch and the way you explain it in a ease. Thanks for such a great video ❤

For say log_base10 (x), I ask myself “How many times do I have to multiply the base number by itself to get x?” And that number would give me my answer. But that still doesn’t help with understanding how to think about logs intuitively and what problems they are capable of solving and why/how they solve the problems.

do you still have that poster link?

Wonderful job. Thank you! I will share with my students.

What is your poster name in background? 😊

Asante sana. Imenisaidia kujua nini hesabu hizi zinamaanisha. Kitu ambacho sikuweza kuelewa wakati nasoma mada hii nikiwa mwanafunzi wa kidato cha pili

Very interesting and well presented in a clear voiced…subscribed!

I like this guy!

Excellent video. What I'm not clear on is the following: the region around eigenvector [-1, 3] becomes saturated with other vectors after applying the linear transformation [M]. Conversely, the region around the eigenvector [2,1] has a relative sparsity of neighboring vectors after applying the linear transformation - what causes this?

ln?

Leaving a comment for the Logarithm....

I guess I'm getting closer to getting it. Next stop, moles

This video was fun and Intresting ! Loved his sense of humor.😆

This was so helpful in conceptualising a concept which has been challenging to grasp. Thank you!

When you distill it, they are just the result of applying manipulations which follow rules on a fictional number system, and doing a lot of pre-calculation. As a philosophy professor I know would probably say, 'Logarithms aren't IN the universe', and so they aren't a cosmic question either.

Historical context helps a ton! Logs are still super important in computation. Lots of computations are done on log scale and only turned back to normal scale at the end. If you don't, you frequently overflow the computer and can induce other numerical issues. As an example, if you work with the gamma function, chances are very good that it's actually represented internally as the log-gamma function because otherwise the numbers get so large you can't store them anymore.

Thank you, I wish I could give it two likes. Lol, so I subscribed instead.

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

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