Outstanding Sir! Not only an understanding of the topic, but a dive into the creation of code that visualizes. I really enjoy your style and the fact that I can learn the concept and how to express the concepts in a coded model. Thanks much!
Thanks for making this. I'm still out of the loop and it will take me some time to digest but I just want to appreciate the animations, voice over and script. I like how you dumb things down a bit and toss out academic rigour in favour of accessibility... subbed. Plus aussie representation
So Peter basically shot his web along the spiral at certain intervals, and at some point, as the spiral spun, the strings converged and trapped Strange right in the middle of it?
Love the video man! Just a suggestion, but if you’re able to you should upgrade your mic. I feel like it’s the missing piece to having some top tier content!
Could the spiral of Theodorus be mapped onto an Archimedean spiral, perhaps by adding a rotation parameter to the latter? I have noticed that Theodorus' spiral closely resembles Archimedes' spiral after the first few turns.
Hy Sir You are very talented and your videos are very helpful for the students. I really respectful to you. Kindly sir guide me which softwares you can use to make your Animated video's Thanks to you!
I have a question similar to this concept, the question is if there is a ray going out from the origin and intersecting points on the Archimedes spiral, how can we prove that the distances between the intersections are equal. I'm not really sure how to do this, could you explain?
It's in the definition of an Archimedean Spiral. r = cθ, c is a constant angular rate in terms of Length per angle ... It's a constant distance per angle ... not time ... c = L/θ. So the δr (change in r) is the same for the same Θ, because the Θ's cancel ... δr = (c)Θ = (L/Θ)Θ = L. It is not a rate in regards to time ... It's a rate in regards to an angle in space ... maybe that is where you got confused? To draw it faster or slower you would use the rate ... Θ/t ... like rpm (revs per minute) where t = time.
@@burger_kinghorn with a constant slope m ... where b is the constant delta r (assuming you understand y=mx+b as the linear equation right?) ... yes, it's basically a polar transformation of a first order polynomial. I say it that way to leave room for logic based extrapolation. Where there exists x , x itself can be a function x = f(u).
@@ejrupp9555 what would be an example of a polynomial in polar? A quadratic ax² + bx + c has slope (1st derivative) 2ax + b. It's no longer a constant but depends on where along the x-axis you are.
@@burger_kinghorn substitute for x, r cos Θ and for y, r sin Θ. It won't look pretty. Set = zero ... 0 = a(rcosΘ)² + [b(rcosΘ) - rsinΘ] + c. Remember it's really y=ax²+bx+c, so 0=ax² + (bx-y) + c. You have to subtract y (or rsinΘ in this case) to equate it to zero. Use the quadratic formula for r ... a = a cos²(Θ), b = b cos(Θ) - sin(Θ), c=c. So ... {sec²(Θ) [sin(Θ) - b cos(Θ) ± √((sin(Θ) - b cos(Θ))² - 4ac cos²(Θ)]}/2a is the general formula. bx-y = r(bcos(Θ) - sin(Θ)) is where you get the b for the quadratic equation incase you were wondering, because you have to subtract, r sin(Θ) from b r cos(Θ). You have to group the x-y term together. (Is that where you were having trouble?)
Although this was not what I was looking for, here are some thoughts «I wanted deductions of formulas (of spirals) and maybe explanations of those and applications» The Pythagoreans, way before Archimedes had discovered the formula for the sum of n terms of a Geometric progression. So Archimedes could have easily found the limit of the series just by elevating to a very high exponent, such as 10,000 «a myriad». He could then could have argued with his heuristic exhaustion concept of incommensurables «which after Cavalieri, Leibniz would call infinitesimals (1900 years later)» that the 'rest' was negligible and could not be greater than 4/3, this was done by setting an upper greater and a lower smaller limit which were greater or equal or or smaller or equal than 4/3, thus it was deducted that that 'should' be the value. Although he would argue that there was always left a residue because (Ai - An*q^n)/(1 - q) entails that q^n if q is between something incommensurably small «as he would argue (there was no 0 number), or an infinitesimal» and 1, say 1/2 and n is VERY great, then (1/n)^n tends to be negligible, because it is too small, thus (Ai - An*q^n)/(1 - q) becomes Ai/(1 - q) which would yield 1/(3/4), which is 4/3. Everything that that mathematician and scientist did «or many other Ancient Greek mathematicians, even since Thales and Pythagóras» that was passed on through millennia is translated even into English «I mean entire Books! His complete Oeuvre was not entirely preserved though, unfortunately», and everything is stated according to principles that once accepted, the conclusions follow logically and axiomatically «in his time, Mathematics had passed through the influence and works of Eudóxos and Eukleídês, which had given books which gave mathematical theorems and propositions a complete theoretical and axiomatic framework, of which with time it was greatly perfected». Leibniz, Huygens, Fermat, Cavalieri did not surpass much, although advanced of what renaissance recovered, and the Work Stoichéia «The Elements» of Eukleídês were only supassed in the end of the XIX century.
I would imagine with a conditional statement. Ie, if vec.get_length > 10: vec.set_color(RED). After the conditional you would scale the vectors in place. I am sure there is documentation of this somewhere.
Nice video, but a bit of a weird format. Always interested in nice manim animations, especially geometryically appealing ones. But merging the code and the topic feels a bit disjointed.
