blackpenredpen, math for fun, blackpenredpen..., / blackpenredpen , blackpenredpen@gmail.com
Пікірлер: 90
@Pamekimo6 жыл бұрын
minus Y, plus Y also say bye bye
@General12th6 жыл бұрын
+
@alitrux6 жыл бұрын
I subscribed for blackpenredpen, not for blackpenredpenbluepen. I am very dissapointed.
@General12th6 жыл бұрын
I think redpenblackpen is _way_ better than blackpenredpen.
@blackpenredpen6 жыл бұрын
Alitrux i am sorry........ : )
@williamtachyon26306 жыл бұрын
In 2019, it may be that his name will be blackpenredpenbluepenyellowpengreenpenorangepenpurplepen.
@VerSalieri6 жыл бұрын
I never understood that blackpenredpen thing, why not just use blackredpen^2? It just doesn’t compute to me..
@TheYoshi4636 жыл бұрын
Is it commutative though?
@chesteezy51976 жыл бұрын
My Number Theory professor disagreed with the theorem after I told him what it was. LOL
@balajishankar6 жыл бұрын
Fantastic.....especially the second part of the proof!
@blackpenredpen6 жыл бұрын
Thanks!!
@Klayx_2 жыл бұрын
night before maths exam. this man is amazing
@akshat92826 жыл бұрын
Instead of saying that taking a point in the minor arc would be no good, you could have just stated why. It's a basic explanation and you just subtract both angles by 360°. Btw I had this in my curriculum 5 years ago and I still haven't forgotten this beautiful theorem wow good job bprp
@varunmurali56716 жыл бұрын
Akshat K Agarwal can u elaborate your statement? I didn't understand subtracting 360 from the 2 angles (I also don't know which two angles you are talking about)
@akshat92826 жыл бұрын
Varun Murali sure. Say you're given that the angle of the minor arc AC is 60° and the point B is on the minor arc instead of the major arc. Then then angle ABC(the angle inside the circle) would be 150° since you can consider the central angle as convex. So it'll be 300° (because 360°-60°). And using the same theorem, the angle ABC becomes 150°
@ingiford1757 ай бұрын
The proof I like most is the one that starts with A&B on opposite sides of a diameter. Once you prove that, you can prove the other two cases you have quickly.
@ThePowerfulOne076 жыл бұрын
Love geometry theorems and concepts!
@dishwasherdog8 ай бұрын
I wish I was you brodi. Imma fail this Damn test
@holyshit9222 жыл бұрын
We can use it for writing equation of angle bisector but it will be a little bit longer than comparing distances of point from both rays of angle
@yaleng45973 жыл бұрын
our school requires us to write angle at centre twice angle at circumference
@ankaparnahajova6 жыл бұрын
Precisely my thinking, I like to show precisely these three variations. Thank you for the video.
@MA-mp5mx6 жыл бұрын
Why are you keep this name blackpenredpen
@gnikola20136 жыл бұрын
You forgot the prove the case when the segment AB colinear to the segment AO!!
@gnikola20136 жыл бұрын
Thanks! lol
@kkkkkkkk11796 жыл бұрын
On that figure, OB=OA(radius) => OBA=OAB=x(let) 180°=AOB+OBA+OCA(angle sum property) =>180°=2x+AOB 180°=AOB+AOC(linear pair) On equating, 2x+AOB=AOB+AOC =>2x=AOC =>2AOB=AOC
@Apollorion6 жыл бұрын
@Kiritsu Insert x=0 in the formula's on the left halve of the board and they describe the situation you suggest.
@qqqquito6 жыл бұрын
Picking a point on the minor arc AC is still good. In which case, the central angle AOC is a "reflex angle", and the inscribed angle ABC is an obtuse angle and is half of the reflex angle AOC.
@HWMREWesker6 жыл бұрын
Stuff from the 8:40 point is unnessecary. Angle AOB equals (180-2y+2x) from AOB triangle. Angle COB equals (180-2y) from COB triangle. Angle AOC equals angle AOB minus angle COB and that's (180-2y+2x)-(180-2y)=180-2y+2x-180+2y=2x, Q.E.D.
@AndDiracisHisProphet6 жыл бұрын
crap, this is obvious -.- I feel embarrassed now
@General12th6 жыл бұрын
Yeah, it actually makes way too much sense...
@debrajbanerjee92766 жыл бұрын
What is the integral of sqroot(sinx) from 0 to pi? I found it 2√(2/π)(gamma(3/4))^2 in wolfram alpha which seems very interesting.can you provide me the magical steps?
@akshat92826 жыл бұрын
Substitute tan(x/2) = u and you'll get everything after that
@debrajbanerjee92766 жыл бұрын
Akshat K Agarwal after this substitution the integral would be 2sqrt(2u/(1+u^2)^3) which would not work
@akshat92826 жыл бұрын
Debraj Banerjee what no. Differentiate the substitution. You'll get (1/2)sec^2(x/2)dx=du Then change the sec to tan if you want. I'm sure you can figure out what to do next if you talk about gamma in your integrations
@akshat92826 жыл бұрын
Debraj Banerjee also if you graph the function, you'll notice that it is symmetric at x=π/2 so computer the integral to that point maybe and then multiply by 2 because at π/2,you can use a property of definite integrals and change u from u to π/2 - u This is a higher level integral and I don't think he'd be able to cover it anytime soon. If you need help, you can still ask or Google it. All the best
@akshat92826 жыл бұрын
Hilbert Black yesss
@thetophatgentleman46345 жыл бұрын
The day blackpenredpen did simple things.
@holyshit9223 жыл бұрын
I use central angle theorem for construction regular 2n gon after construction n gon with given side length
@teekayanirudh6 жыл бұрын
I think until 5:45 was the essential part of the proof, since if we join A and C we get a chord AC of a circle and angles subtended by a chord of a circle on it are all equal. But I really like that you did the other case as well for completeness :)
@randomname9291 Жыл бұрын
I’m pretty sure that that sentence derived from the central angle theorem and not vice versa
@bilalabbad79542 жыл бұрын
The geometry is incredible
@Intskints6 жыл бұрын
Now it makes sense how Thales thm works, cause the diameter's central angle is 180 degrees.
@UnathiGX6 жыл бұрын
Yay...I just learned a new trick..Thanks BPRP
@chessandmathguy6 жыл бұрын
Beautiful.
@blackpenredpen6 жыл бұрын
steamroller82 yay!!!
@tangentofaj6 жыл бұрын
Hopefully you like this? I LOVE THIS.
@wowfmomf61266 жыл бұрын
Thanks for the daily doze of math
@labyrinth60916 жыл бұрын
When i was 13yo just solved it in like 20 sec, but now with 24 i couldn't. Is that bad?(don't know what to feel)
@frederickm98236 жыл бұрын
In the second case, why didn't you use the triangles OCB and AOC. The OCB one gives you the angle on the right side (180-2y) and the AOC one gives you the whole angle (180-2*(y-x)), so the angle we are looking for is: 180-2*(y-x) - (180-2y) = 180-2y+2x-180+2y = 2x Therefore the angle in the middle is twice as big as the one on the outside. Yet I liked your way, too, but it was a bit too complicated, I guess
@typo6916 жыл бұрын
Hey can you tell me why that angle is y - x? EDIT: Nevermind, I understand now. It looked confusing because of the dimensions of the diagram, I forgot that it was isosceles.
@typo6914 жыл бұрын
@Anurag MFT OC = OB so if OCB = y then OBC = y cause it's an isosceles triangle. Then it's easy to see that OBA = y - x
@pipithandayani11 ай бұрын
for the real life, what the situation we can explaint about this theorem?
@purim_sakamoto3 жыл бұрын
へええ これはみんな覚えとくと便利だねえ😄
@darshnavijay43395 жыл бұрын
Best explanation
@General12th6 жыл бұрын
If I squint my eyes and tilt my head, your diagram kinda looks like a pentagram.
@migtrewornan80856 жыл бұрын
If point B coincided with point C wouldn't the angle ABC be zero. In that case angle ABC must approach zero as B approaches C and hence cannot be constant?
@tigerbeast34065 жыл бұрын
Point C is kinda like the border between the big AC arc and the small AC arc. Point B, as we know, must be on the big AC arc. The theorem doesn't work if point B is on the small arc or on its borders. If point B and point C are on the same place, the angle ABC is 0, but the theorem is not appliable for this case. Even if point B is very close to point C, as long as it is on the big arc, angle ABC is two times smaller than its corresponding central angle.
@marcypan82194 жыл бұрын
I FINALLY UNDERSTAND THIS!!!!!!!!!!!
@sharnezhu28604 жыл бұрын
let us peep the shoe game
@JorgenJorgensenSonofJorgen2 жыл бұрын
Is there a way to prove this without splitting into multiple cases?
@abhivish20176 жыл бұрын
Nice explanation sir.....
@Sid-ix5qr6 жыл бұрын
I was taught that Central Angle in a Circle was always 90°.
@noorashfaq39782 жыл бұрын
'semi circle...
@gowrishi18994 жыл бұрын
nice rhyme in 10:19
@SuperSatyasrinivas4 жыл бұрын
Good
@mdmuktadi79802 жыл бұрын
Cool bro
@billy.71136 жыл бұрын
Why don't you just write ∠AOC = 2∠ABC instead of m∠AOC = 2m∠ABC ? m is confusing.
@madamehajj28166 жыл бұрын
What about interior angle
@williamtachyon26306 жыл бұрын
Great video, as always. I really love mathematics, isn't it! :)
@andrewjustin256 Жыл бұрын
7:40 why is this angle y-x?
@sergioavramescu Жыл бұрын
Because it is an isosceles triangle, the angles OCB and OBC has to be the same
@basilemaddalena15866 жыл бұрын
Hi, can you figured out the derivative of n ! ?
@hattorikanzo27935 жыл бұрын
Yes
@zhandexiang222 Жыл бұрын
how did the y-x come to be
@xmatterx92466 жыл бұрын
Yaaaayyyyyyy
@kaaiplayspiano72004 жыл бұрын
What?
@retired55486 жыл бұрын
i guess you can say that it's a central theorem for angles in a circle
@notananimenerd13333 жыл бұрын
K
@DjVortex-w6 жыл бұрын
That's the Star Trek symbol...
@BigDBrian6 жыл бұрын
but what if B is on the left side instead of the right side :^)
@TheReaper95206 жыл бұрын
You can get around that by slapping a WLOG onto the second scenario ::^^))))
@stevethecatcouch65326 жыл бұрын
Copy his proof on the inside of a window, then look at it from outside.