That's amazing and interesting. I cant help but imagine splitting the diameter of the yellow circle into endless small circles, and think, wouldn't that make the diameter aspire to be the same as half the circumference?...
@jash21222 yes I can understand that, but I can't do calculus, and it seems to me (just a thought) that if you divide the diameter to infinite circles, the resulting calculation may end up making the diameter equal to (or rather, reaching towards) half the circumference of the larger circle? I don't have to tools to test this. It's just an idea
@@DavidMauaswhat? Half of the circumference of a circle divided by the diameter is always equal to π/2 which may be close to 1 but definitely isn't equal to 1
@@DavidMauasTake a square with side length 1 and place it on a circle with a diameter of 1. Fold the corners into themselves infinitely many times (this preserves length) and watch. It'll approach the shape of the circle. But the circle would have a circumference of pi, while the square would have a perimeter of 4. Does this mean that 4 = pi? No, the resulting shape is "crinkly" (I'm not sure what this means formally either, I just know it to be true). The same would happen with divvying up this circle.
@DavidMauas I think just knowing the circumference is 2*pi*r would tell you Since every time you split it up the combined radii ar the same as the radius of the original circle
@@jacobwestbrook9527 yes, but I think of how limits are used (I am not well versed in math to speak in equations, so excuse my pseudomath) - if 1/2 + 1/4 + 1/8 ... Is equal to 1... Then it follows logically that the same would happen to the circumference of the circles as they grow smaller and smaller edging towards the diameter... Do you follow my meaning?
You could also just go by diameters: Call the diameters of the red circles a and b, then the sum of their circumferences is aπ + bπ. The circumference of the outer circle is (a + b)π. This expands to aπ + bπ, hence the two are equal. Further, this shows that any number of circles of arbitrary diameter can be lined up along the diameter of a larger circle in this manner and their circumferences, (aπ + bπ + cπ + dπ + ...), will always sum to that of the larger one, π(a + b + c + d + ...).
I just verified that the formula for the circumference is directly proportional to the radius. (A constant times the radius) Since it is, then no matter how many pieces you subdivide, the total circumference stays the same. Since the total sum of the radiuses remains the same, the circumference remains the same, as the circumference is a constant multiple of the radius for each circle. I can do the math to prove it, but the quick sanity check verifies things. The math is simply: x(a+b) = xa+xb by the distributive property of multiplication over addition. And x here is simply π where a, b , and (a+b) are the diameters.
so fascinating! Taking more than two small circles, actually taking an infinite number of infinitesimal small circles, it appears to be a "line" with the length of and appearance of "d" of the big circle - still this "line" (containing the extremely small circles) will still be the length of the circumferrence of the big circle! Amacing! How beautiful math realy is! ❤
let x & y= diameter of small circles respectively let d=diameter of yellow circle=x+y ------- 1 Circumference of yellow circle=pi×d ------ 2 Circumference of red circles= pi×x+pi×y = pi(x+y) by eqn 1 = pi×d = eqn 2 HP
This is the same equation that demonstrates that a smooth earth with a length of rope that fitted exactly around the earth at the equator and an extra length of rope that was 2Pi meters long was added, then the rope could be suspended to a height of 1 meter all around the earth.
I never thought of that but I am guessing that would hold true for any number of circles because smaller diameter equals smaller circles proportionately. 🤔🤔🤔Hmm
Hii. Can you remind me why the formula was 2pi A and not just piA. Becouse I only remember that the curfice of the circle is equal to the radius multiplied by pi (3,14). I just heve seem to forrgoten if it was this or the half curfice of the circle.
No ...measure it Its not 2π(3.3333333) its 2Rπ(3.3333333) π(3.333333333)•d(a)+π•d(b)=D•π(3.3333333) not 3.14 Test it with a measure. Just entertain me. U think ur correct, entertain yourself. Please.
Correction: when writing the circumference of the red circles, you called them radius. You said “the *radius* of the small red circle is 2πa and the *radius* of the big red circle is 2πb”. Instead of “radius” you meant to say “circumference” because the actual radius are “a” and “b”, respectively, without “2π”.
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
Best thing I’ve seen today, how did I not know this. Truly beautiful.
Explains it so smoothly, math natural for this professor
That's amazing and interesting. I cant help but imagine splitting the diameter of the yellow circle into endless small circles, and think, wouldn't that make the diameter aspire to be the same as half the circumference?...
@jash21222 yes I can understand that, but I can't do calculus, and it seems to me (just a thought) that if you divide the diameter to infinite circles, the resulting calculation may end up making the diameter equal to (or rather, reaching towards) half the circumference of the larger circle?
I don't have to tools to test this. It's just an idea
@@DavidMauaswhat? Half of the circumference of a circle divided by the diameter is always equal to π/2 which may be close to 1 but definitely isn't equal to 1
@@DavidMauasTake a square with side length 1 and place it on a circle with a diameter of 1. Fold the corners into themselves infinitely many times (this preserves length) and watch. It'll approach the shape of the circle. But the circle would have a circumference of pi, while the square would have a perimeter of 4. Does this mean that 4 = pi? No, the resulting shape is "crinkly" (I'm not sure what this means formally either, I just know it to be true). The same would happen with divvying up this circle.
@DavidMauas I think just knowing the circumference is 2*pi*r would tell you
Since every time you split it up the combined radii ar the same as the radius of the original circle
@@jacobwestbrook9527 yes, but I think of how limits are used (I am not well versed in math to speak in equations, so excuse my pseudomath) - if 1/2 + 1/4 + 1/8 ... Is equal to 1... Then it follows logically that the same would happen to the circumference of the circles as they grow smaller and smaller edging towards the diameter... Do you follow my meaning?
You could also just go by diameters:
Call the diameters of the red circles a and b, then the sum of their circumferences is aπ + bπ. The circumference of the outer circle is (a + b)π. This expands to aπ + bπ, hence the two are equal.
Further, this shows that any number of circles of arbitrary diameter can be lined up along the diameter of a larger circle in this manner and their circumferences, (aπ + bπ + cπ + dπ + ...), will always sum to that of the larger one, π(a + b + c + d + ...).
Why not calculate circ. of small circles as aπ and bπ where a and b are diameters? Then circ. of big circle equals π(a+b) = aπ + bπ?
I wanted to show both formulas for circumference of the circle.
Smart. Simple. Love it.
Really cool. Thank you !
That was awesome! Love Euclidian Geometry!
That was fun
That's impressive. Thanks
Thanks, it is great to be reminded of these things
Great bonus question for a test.
Amazing math wizard ❤
Beautiful, I love math.
As my high school physics teacher used to say: so simple, and yet so straightforward.
Haha. 🤦🏽♂️. It all made sense at the end. I got wrapped up in the problem 😂
If i had this teacher in secondary school. I would be changing the world now.
Y hasn't this man not nominated for nobel Prize..
Flabbergasted
I just verified that the formula for the circumference is directly proportional to the radius. (A constant times the radius)
Since it is, then no matter how many pieces you subdivide, the total circumference stays the same.
Since the total sum of the radiuses remains the same, the circumference remains the same, as the circumference is a constant multiple of the radius for each circle.
I can do the math to prove it, but the quick sanity check verifies things.
The math is simply:
x(a+b) = xa+xb by the distributive property of multiplication over addition. And x here is simply π where a, b , and (a+b) are the diameters.
so fascinating!
Taking more than two small circles, actually taking an infinite number of infinitesimal small circles, it appears to be a "line" with the length of and appearance of "d" of the big circle - still this "line" (containing the extremely small circles) will still be the length of the circumferrence of the big circle!
Amacing! How beautiful math realy is! ❤
let x & y= diameter of small circles respectively
let d=diameter of yellow circle=x+y ------- 1
Circumference of yellow circle=pi×d ------ 2
Circumference of red circles= pi×x+pi×y
= pi(x+y) by eqn 1
= pi×d
= eqn 2
HP
Excellent video wonderful 😊😊😊😊😊😊❤❤❤❤❤😊
You can use a rubberband to illustrate this. Turn a rubberband from the shape of a circle to the shape of 8.
That's good a way of looking at it.
@@mrhtutoring Thanks!
but those triceps's
Damn that was quite observant!!! 😊
Mr htutoring. An amazing mathematician 🎉
선생님, 재밌게 보고 있습니다. 감사합니다.~^^
재미있게 봐주셔서 감사합니다. 😊
Fire proof 🔥
At the beginning you can notice that both c=c, so the length of the circles are identical
Pretty fricking cool
Cause the ratio of a diameter to circumference is π so if π necer changes you just need the diameter theta to equal diameter
This is the same equation that demonstrates that a smooth earth with a length of rope that fitted exactly around the earth at the equator and an extra length of rope that was 2Pi meters long was added, then the rope could be suspended to a height of 1 meter all around the earth.
is that is theorem or something, ?
means 2 circle on diameter of filling length have same C
Yes, it's true for any number of circles
@@mrhtutoring thank you sir, I'm preparing for my CAT exam and it helped me... ❤️
I never thought of that but I am guessing that would hold true for any number of circles because smaller diameter equals smaller circles proportionately. 🤔🤔🤔Hmm
I like the colored projection on the chalkboard!
I was watching in black and white . 😶
I wish he taught math when I was in school.
Sir this question plz differentiation of x^y+y^x=2
makes sense
i suppose this can be the proof for the saying "if i fits, i sits", no?
(pi × d1) + (pi × d2) = pi × (d1 + d2)
Without calculating I say same
Hii. Can you remind me why the formula was 2pi A and not just piA. Becouse I only remember that the curfice of the circle is equal to the radius multiplied by pi (3,14). I just heve seem to forrgoten if it was this or the half curfice of the circle.
Circumference of the circle is pi•d, where d is the diameter.
Since d=2r, where r is the radius, the other formula for Circumference is 2pi•r.
Sir please help
If F(X) = 1/√2x-1
Then
F-1(-1) is defined or undefined
How did circumference of yellow circle became pie d , can anyone explain pls
There are 2 formulas for circumference of a circle.
2πr and πd.
Since the diameter, d, is 2r.
Shouln't d be equal to a+b and not 2a+2b as we need radius, not diameter?
he used a different formula, pi*d, which uses diameter and not radius
well technically its the same formula because 2r=d
C = 2πr and C = πd is correct, because d is equal to 2r
No ...measure it
Its not 2π(3.3333333) its 2Rπ(3.3333333) π(3.333333333)•d(a)+π•d(b)=D•π(3.3333333) not 3.14
Test it with a measure.
Just entertain me.
U think ur correct, entertain yourself.
Please.
Pi is 3+⅓/3+ ⅓/(⅓/3) 3.33333
3/1+1/3 or. 3.333
TRUST IT. TRY. JUST TRY WITH A TAILORS RULE
WOW, that is so boring!!! NOT!!! (SAME SAME)
Correction: when writing the circumference of the red circles, you called them radius. You said “the *radius* of the small red circle is 2πa and the *radius* of the big red circle is 2πb”. Instead of “radius” you meant to say “circumference” because the actual radius are “a” and “b”, respectively, without “2π”.
Well I immediately knew they had to be equal, but he lost me with the calculations. Anyway...
???😅
You twice said "radius" instead of "circumference".
Nice
❤