Extremly underrated channel!!!

@betabeast12

5 жыл бұрын

I agree!

Damn the proof was way simpler than I expected.

I'm sad that what I enjoy in a few minutes must take you so much work. Incredibly fantastic content. If you're enjoying it, please keep going - I'll have to become a patreon.

@ThinkTwiceLtu

6 жыл бұрын

thank you. Any kind of support is greatly appreciated~

@sajaltuley1578

2 жыл бұрын

@@ThinkTwiceLtu it is true only for equilateral triangle?

@jf2801

Жыл бұрын

​​@@sajaltuley1578 I'm no mathematician. But, I'd say most likely, yes. Because, in order for it to work, all sides probably should be the same length and each angle should be the same. This is just a guess, though. Since that would also make each side an equal distance from the center point, which is the initial position of the dot.

In the middle of my binge watch of your channel. Your channel is going to blow up soon. Like 500k by 2019 or something?

@ThinkTwiceLtu

6 жыл бұрын

Sam Nel haha, well that would be pretty awesome but I think it's quite unlikely. thanks for support

@pikerpoler

6 жыл бұрын

It will blow up. Especially now after 3blue1brown mentioned you in one of his vids.and Your stuff is really good :)

@aca792.

6 жыл бұрын

i came her because of 3b1b think twice is cool!

@ianprado1488

6 жыл бұрын

Even at 500k, this channel would be underrated

@doornumb

5 жыл бұрын

Sadly, no

I think there is a better explanation that uses pure visualization, no area formulas. So starting with the three perpendicular lines, first draw a horizontal line through the point. This splits the triangle into two sections: the base and an upper equilateral triangle. Rotate the upper triangle 60 degrees clockwise. Now draw another horizontal line through the point (which has been rotated 60 degrees as well), splitting the upper triangle into another two pieces. Rotate the topmost triangle 60 degrees clockwise. Now we have rearranged pieces of the triangle such that the shape of the triangle hasn't changed, but all perpendicular trisectors line up vertically, showing that they add up to the height

@kaustubha7371

5 жыл бұрын

Maths is so fun a beautiful

@rium5PA43R

5 жыл бұрын

Nice alternate proof. I guess when you rotate the upper triangle, you rotate around its center. I think the angle of rotation is actually 120 degrees rather than 60.

@metametodo

5 жыл бұрын

I wish I could visualize that too

@betabeast12

5 жыл бұрын

But the upper triangle is not equilateral.

@avikdas4055

4 жыл бұрын

@@betabeast12 You are wrong. The upper triangle would be equilateral too. Nice proof tho.

Damn! I'd never have thought that it'd be this simple a proof... I mean, just 2 steps???

Your videos explain so well, and I liked the fact the the point wasn't "static", so it was always moving so we could see that it was always true =D. And again the music fits well in the video! hahaha

@ThinkTwiceLtu

6 жыл бұрын

Nuno Mateus Hey, glad you liked this one. I tried to make the explanation as simple as possible. The making of this video had many trials haha.

@vpambs1pt

6 жыл бұрын

I believe! And at the end you always manage to do it the best way! Btw is this music from a famous movie or something? it looks like! I'm starting to like it!

@ThinkTwiceLtu

6 жыл бұрын

tbh I don't know where the music is from. I found it on KZread by chance haha. But ya I think it sounds nice

this is the only one that I can explain before you tell me how to haha I'm proud lol

@ThinkTwiceLtu

6 жыл бұрын

Lucy Luo you're too good tbh

@lucyluo497

6 жыл бұрын

thank you!

@ThinkTwiceLtu

6 жыл бұрын

Lucy Luo just kidding 😁

@atharvakulkarni0

6 жыл бұрын

No, I am also able to.

@marcgrec7814

6 жыл бұрын

bamboozled

I just love you animations and your explanations are so simple and cool, thanks!

@ThinkTwiceLtu

6 жыл бұрын

estuardoremi great to hear that!

Truly great videos. I've seen every video. Most more than once. Please keep making more!

Beautiful proof. Congrats!

I love this channel... This channel has both mathematics and science, which I love. And the way of the video is interesting, unlike other channels whose science and math content are boring...

wait no cause this is actually so cool and just really fascinating I love the visualizations too!1!1!!

I've always been ass at maths why do I find these videos so interesting

This is such a great channel. Subscribed!

This is just so beautiful.

Very nice and simple proof. Video helps understand the proof very easily. Well done

Excellent video, I'll never forget Viviani's Theorem

Excelent theorem, excelent proof, excelente channel! Thank you

very lucid and simple... moreover very interesting also

Great thanks a lot for this video 👍 I saw complicated in the notation and hypothesis

learned something new, thanks!

You deserve MILLIONS of subscribers because you show the world what math is really about.

Gorgeous 💖

You made this theorem a tablet. I watched it and it took less than 2 mins to understand. The world needs more doctors like you

This channel deserves more attention

Awesome.

Beautiful!

Beautiful

Why isn't this channel not popular

I've been following your channel for a while and never failed to be surprised by the elegance of your animations -- presenting mathematics so well visually and simply! Thank you for you amazing talents~

This is great content!

Nice! Very interesting... well done

@ThinkTwiceLtu

6 жыл бұрын

breno moraes thank you:)

Just awesome ❤️

Love this channel

Excellent content.Keep up the good work

@ThinkTwiceLtu

6 жыл бұрын

thank you!

Very informative and beautiful

That was so quick and simple that one ends like doubting that this could be the real answer lol

Love it!

Very satisfying!

THIS IS THE COOLEST THING I'VE SEEN IN A WHILE

@ThinkTwiceLtu

3 жыл бұрын

:)

Man your animations are awesome

@ThinkTwiceLtu

6 жыл бұрын

There's a nice way to do this without areas - notice that you can shrink the triangle on one side until that side touches the point, and this reduces the height by the same amount it reduces the sum. By doing this twice, the point is at a vertex of the triangle, and the one remaining non-zero term in the sum is the length to the opposite side, which of course is the height of the remaining triangle.

Subscribed. I don't subscribed to channels that easily. I sometimes unsub from time to time. But when I stumbled upon this channel, insta-sub!

love it

Thanks so much

This is beautiful. :-)

@ThinkTwiceLtu

6 жыл бұрын

Kylie Estrada ☺️

Really good

Curiously, I discovered this theorem myself about 30 or 35 years ago, and later learned I had not been original. However, my original theorem spanned not only triangles but any planar regular polygon: the sum of distances from an inner point to all the sides of a regular polygon is invariant. If a polygon has an even number of sides, it is obvious that the sum of distances from an inner point to both a side and its opposite is constant, hence, so is such a sum of distances to all the sides. But I didn't know of any such easy proof when a regular polygon has an odd number of sides. Now your video and proof give me a way to prove my general case.

Wonderful.

Nice 👏👏

Beautifull

와 진짜 지린다 유익한 영상 감사합니다

Nice!!!

truly one of the moments of all time

Amazing

You earned a subscriber.

Awesome!

@ThinkTwiceLtu

6 жыл бұрын

Mohammed Sharukh :)

It is not new to me. But I love how you demontrated the problem and solve it. Hope you keep up and mix in with some more complicated problem.

So good

Super nice video!! Your efforts are really appreciated, if you could make a video like these for all geometry theorems in Olympiad it would be pretty cool and I guess would blow up pretty fast. I know it takes a tremendous amount of efforts so thanks!!! (PS how do you animated your videos?)

I feel dumb now for being surprised at how simple that was. Well done!

Wow, how did I JUST find this channel when looking for some inspiration for a lesson?...

I could visualise your hardwork too along with this content

Your video prompted me to an alternate visualization (though it may be more difficult to establish). At 0:57 when black lines replaced coloured perpendiculars, I began to see the animation as an observer hovering over a tetrahedron (perhaps the width of the perpendiculars being less than the width of sides helped create that 3D effect). If one could establish that the collection of triangular projections seen by an observer hovering over the tetrahedron at different angles would cover all possible collections of triangles made by shifting the point in the triangle, one could prove that the sum of perpendiculars is constant.

That blew my mind.

Awesome

brilliant

Really enjoying the telltale music

hey think twice ! if you reading this than thankyou for great explanation and efforts

@ThinkTwiceLtu

3 жыл бұрын

Thanks for watching:)

Great doing well job keep it up I am fan of it,sir please upload video on ramanujan numbers

Awesomeeee

@ThinkTwiceLtu

6 жыл бұрын

yay :)

Neat!

Met your channel by a comment on another video, the you tube algorithm is failing you! I demand viewing justice!

why is so underrated?

More of this please

@ThinkTwiceLtu

6 жыл бұрын

erozi OK

Another gem. How's your health? Continuing to improve I hope!!

@ThinkTwiceLtu

6 жыл бұрын

dubarnik thank you. Well it's still pretty much the same as before. But hopefuly it will get better soon.

@lucyluo497

6 жыл бұрын

get better xx

@ThinkTwiceLtu

6 жыл бұрын

Lucy Luo thanks ☺️

I like how catchy this is in x2.

with this music all is more epic

Area of any triangle is (base × height) ÷ 2. So break up an equilateral triangle with height "H" ( 🔺️E ), into 3 triangles of different heights ( 🔺️1, 🔺️2, and 🔺️3 ). We are trying to prove that the sum of the 3 perpendicular distances from any point inside an equilateral triangle must equal the total height of the equilateral triangle, by using the proof: Area of 🔺️1 + Area of 🔺️2 + Area of 🔺️3 = Area of 🔺️E. Each perpendicular distance from a point inside the larger equilateral triangle can coincidentally be used as a value of each of the 3 smaller triangles' heights. The heights for each one is: h1, h2, h3, and H. And each triangle 🔺️ has the same base, "B". Each area is: ( base × height ) ÷ 2. And so it must be true that: ((B×h1)÷2) + ((B×h2)÷2) + ((B×h3)÷2) = (B×H)÷2, They all are being divided by 2, so it must also be true that: (B×h1) + (B×h2) + (B×h3) = B×H, And the base, "B" is the same for all triangles in this case, so factor it out. Therefore it must also be true that: h1 + h2 + h3 = H. So Viviani's Theorem is proven mathematically that the 3 perpendicular distances at any point inside of an equilateral triangle must equal the total height of the equilateral triangle.

Neat.

B-E-A-utiful

when explained in a way that makes sense how, infinity simultaneously is forever and finished, ....all problems will be solved

@ibrogamingman8591

6 жыл бұрын

anyone agree

Can you do one with the given point not moving and move the triangle instead? I want to see a three dimensional analysis

Mathematical observation shown here are like lost spells which every Wizard of math wants to find. :)

Question When we put the point on the bottom of the triangle, surely length point-to-top = height. Right? That, plus other lines' length wouldn't the total length be longer than the height then?

@ThinkTwiceLtu

6 жыл бұрын

if you put the point at the bottom of the triangle, the length of a line from the base of the triangle to the point would be 0. So there would only be two lines to add up, which will be equal to the height of the triangle

@imnash8711

6 жыл бұрын

Think Twice oohh I get it now . Thanks

I dunno, just prove it for the edge cases and then use the mean value theorem??

how about the iregular triangle ? same process?

why does that to be an equilateral triangel only, same thing can be done for scalene right?

does this work for nonequilateral triangles? i think not

good

Is it just me or the triangle moves in 3D when the sides are colored? O_o *soooo good*

Is this true for any triangle or just equilateral triangles?

What do you use to animate? Blender?

Sir viviani theorem is only valid for only equilateral triangle right .. And thank you for the video sir 😌❤️❤️👊

I proved it by adding the areas

This damn song gives me sad nostalgia

wow

Was it said anywhere that the triangle was equilateral?

1:00 that looks a lot like a 3D triangle-based pyramid, wonder if it is related