Formula for the Area of every Shape | Pick's Theorem

  Рет қаралды 15,689

Digital Genius

Digital Genius

Күн бұрын

Пікірлер: 40
@jhonlawrencebulosan741
@jhonlawrencebulosan741 Жыл бұрын
Why doesn't this channel have more views? This is very educational!
@ErdemtugsC
@ErdemtugsC Жыл бұрын
1: early start 2: .. algorithm hates him
@gundagaming69
@gundagaming69 10 ай бұрын
Yess​@@ErdemtugsC
@samueldeandrade8535
@samueldeandrade8535 6 ай бұрын
What is really good doesn't get views.
@Fire_Axus
@Fire_Axus 3 ай бұрын
it is unnoticeable
@harshsrivastava9570
@harshsrivastava9570 Жыл бұрын
Awesome video! The explanation was very clear and helpful. You deserve a lot more views!
@sm64guy28
@sm64guy28 Жыл бұрын
The quality of these videos are insane compared to its number of views, keep up the good work
@ChezburgerLeaf
@ChezburgerLeaf Жыл бұрын
How is this channel this small!? You absolutely deserve my sub. 👍
@mrshoebill7859
@mrshoebill7859 Жыл бұрын
This will come in handy! Thank you!
@dogslife4831
@dogslife4831 6 ай бұрын
This video is going to get Millions of views in the future I forwarding it to increase the views
@bijipeter1471
@bijipeter1471 9 ай бұрын
Thank you, so much
@CrimsomGloryXD
@CrimsomGloryXD Жыл бұрын
I feel big brain now
@Fire_Axus
@Fire_Axus 3 ай бұрын
YoFeArIr
@jan-pi-ala-suli
@jan-pi-ala-suli 5 ай бұрын
really calming audio :)
@thehiddengamer
@thehiddengamer Жыл бұрын
what program do you use to make these videos? i want to try making some myself
@CodeOverDoYou
@CodeOverDoYou 5 ай бұрын
It's such an ingenious formula that one Russian mathematician even built a career on it
@cabji
@cabji 11 ай бұрын
does this formula work if the lines between cartesian points are not a straight line? For instance, if you have a kidney shaped pool in a backyard and the backyard is 10 x 10, how much precision is needed to plot points to determine the area of the kidney shaped pool?
@marcuslaurel5758
@marcuslaurel5758 3 күн бұрын
This formula definitely does not work if the lines are curved. This can be seen from the fact that it’s derived from summing areas of triangles. Curving the lines takes away the simple geometry that makes it work.
@lkdragon7941
@lkdragon7941 Жыл бұрын
Continue making videos!
@abcabc-uv6ce
@abcabc-uv6ce Жыл бұрын
If you want to figure out the area from an arbitrary shape you found somewhere you need to work out the grid first to use that method, right? It is possible the grid get very tiny to the point you calculate the shape like you would do it “normally”. But anyway it is still very cool thing to know.
@shreya1159
@shreya1159 5 ай бұрын
Underated
@ednalynpenaranda
@ednalynpenaranda 2 ай бұрын
0:16 what happened
@gmr7901
@gmr7901 6 ай бұрын
решил по формуле Пика за.... хотя, подождите.
@TDomonkos2011
@TDomonkos2011 Жыл бұрын
I love your videos!!!
@dynamiccode1
@dynamiccode1 Жыл бұрын
How do you edit your videos?
@Deltaclass96171
@Deltaclass96171 9 ай бұрын
Great video! But I want a example where the lettuce polygon is very very big and you a very very big hole there too
@poulpimus
@poulpimus Жыл бұрын
I didn't understand how we used specific cases (like 1 or 3 holes) to demonstrate the formula for n holes.
@arthurkassis
@arthurkassis 6 ай бұрын
if you use the formula for a shape with n holes, it will also work, but for a video I think is simpler to explain using examples with an exact number of holes
@bagelnine9
@bagelnine9 Жыл бұрын
Okay, but what about disconnected shapes?
@Qaptyl
@Qaptyl Жыл бұрын
just find the area of both and add together
@panbefi7683
@panbefi7683 7 ай бұрын
i feel cursed. the universe looked upon me.
@tomassanchezmuniii240
@tomassanchezmuniii240 6 ай бұрын
So you're telling me that if it has an infinite amount of holes, the area would be infinite... I don't get the fact that the more holes in the figure, the bigger it will be.
@marcuslaurel5758
@marcuslaurel5758 3 күн бұрын
Inductive arguments do not say something about what happens in the limit. In fact, the argument used here breaks downs as you’d get the indeterminate form infinity-infinity.
@biratuba
@biratuba Жыл бұрын
You only proved that the Pick's Theorem is valido for Lattice-Aligned Right Triangles without boundary points in the hypotenuse, it is not clear how to generalise the argument for general triangles.
@divisix024
@divisix024 Жыл бұрын
Tl;dr: It suffices to consider lattice aligned right triangles, since any lattice triangle can be rotated and then subdivided into two lattice-aligned right triangles by drawing a height from one of the vertices. This means every lattice polygon is the nonoverlapping union of lattice-aligned right triangles, with any two distinct triangles sharing at most one side. The proof follows the merging argument in the video. Suppose the original triangle has B boundary points and I interior points.There are exactly 2 boundary points which lies on the height. Suppose also there are C interior points which lies on the height. Those C points become boundary points when we subdivide the triangle. The areas of the two right triangles are given by the formula, which counts a total of B+2C+2 boundary points and I-C interior points. The sum of their areas is (B/2+C+1)+(I-C)-2= B/2+I-1, but this sum is exactly the area of the original triangle, so the formula does work for any lattice triangle.
@biratuba
@biratuba Жыл бұрын
​@@divisix024 I see 2 problems with this argument. 1. there is no reason for the triangle to keep being latice aligned after being rotated(if for example none of their sides have integers length). 2. even if they do, you would still need to prove that after the rotation the triangle will have te same amount of points inside and on the border. I think the better argument is to take te smallest rectangle that encloses the triangle and observe that it can be separated in to 3 latice aligned triangles and the original triangle
@ChrstphreCampbell
@ChrstphreCampbell 7 ай бұрын
It’s very annoying that you’re Not providing The solutions for all The examples ( ? )
@RunningOnAutopilot
@RunningOnAutopilot Жыл бұрын
You overcomplicated your explanation Once you’ve explained the chain of logic you don’t need to reexplain it every time you can just hop to the end If it requires going through the process again then go through only the pertinent parts of the process
@mathbrah
@mathbrah Жыл бұрын
aka shoelace
@empmachine
@empmachine Жыл бұрын
If you could just speak clearly it would be perfect. It sounds like you are an adult on charlie brown, LMAO!
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