This is a really good video! Interesting how normal Venn diagrams lack the 2 extra spaces. However, I do think that normal 4 circle Venn diagrams are good in some situations. For example, I saw a 4 circle Venn diagram which compares stimulants, depressants, hallucinogens, and anti psychotics. Since stimulants and depressants are opposites, comparing them is not possible. Same goes for the other 2. I think that in rare cases like these where those 2 missing spaces work in favor of the context, it is good. Otherwise, your Peyam diagram is super neat!
Dr. Peyam said you can do this with spheres. That generalizes. For 2 sets, you can use 2 segments. For 3 sets, use 3 circles. For 4 sets, use 4 spheres. For n sets, use n "spheres" of S_n-2. All you need is an n-1 dimensional board to draw on. 😜
What is the highest number you can do with just ellipses? The wikipedia article has a 5 one but is that the highest? Or can you do any number but they get hard to find? Or is it just that with blobs you can just keep adding but with ellipses you have to redraw?
I see something weird... Starting from set C, a circle; set D, a dumbbell; set E, a cross...They just look like the electron orbitals s, p, d. Is that anything relevant or just a coincidence?
@@drpeyam Following the line of thinking, what are sets A and B represent if the diagram is really related to electron orbitals, which by themselves are indeed probabilistic functions?
@Dr Peyam I have a question which I dunno how to solve [q(x)]² = 9x⁴ + kx³ + lx² - 4x + 4 To find : value of (k+l) A little hint how to approach would be enough...
Assuming q(x) is a polynomial, we can assume q(x) to be 3x^2 + cx +2 , can you see how squaring it leads to getting constant term of 4 and leading coefficient as 9, now expand it and compare it with the given equation.
After being cordially invited to consult the Venn Diagram wikipedia page, I remarked that although both the French and the English version of this article mention the existence of Smith's equivalent diagrams of the form y_i = sin(2^i x)/2^i, the French one lists this information as questionnable. When further looking at it, the reference is indirect which makes it hard to verify. Do you have some info whether that's true or not? Also, the Italian and the German one do NOT mention this info and the German one has nice info regarding Venn diagrams and syllogisms. A second remark, the German article made me think that it is possible that what we are taught is more of a Euler-Diagramme in the German sense as it is a "Venn Diagram but it does not have to have all possibilities of intersection represented".
That’s so interesting! I didn’t know there’s a difference between the wiki pages. I generally think that the English one is most accurate, but maybe I’m wrong. Thanks for checking
@@drpeyam There is indeed a lot of differences between languages in Wikipedia. However, they often don't contradict each other but they often explore a problem in different ways. I often check English/French, sometimes German but I am not fluent in it. I had a discussion with it recently regarding the Wikipedia articles for similarity in geometry (similitude) and they are both fairly different in structure. In this case, the problem is different because one of the proof is flagged as questionnable in a language, not questionnable in English and not present in others which is rare. Personally, I do not have enough knowledge to assert whether or not Smith's equivalent diagrams works or not. What do you think about it? Is the source trustworthy?
Nice! I guessed the answer was ellipses correctly!!! Heck only real talented people can draw a circle without there being any eccentricity at all and I'm not certainly one of them so it makes sense the answer should be the more natural occurring as opposed to perfect shape.. Dr Peyam what is your favorite Non Euclidean geometry?
What do you mean by fully connected? A complete graph? Unlikely to be connected to it anyway since they overlap. Would have loved a graph theory connection though since that's in my top 3 branches of maths. You certainly could do a graph with coloured paths where each is one case (single ones can be a loop)
Forgive me, but who said that sets are represented only with circles in Venn diagrams? In Venn diagrams, any closed form can be used to represent a set.
I had played the game "Keep Talking and Nobody Explodes and in the free to access webpage necessary to play the game it shows you a 4 ellipse Venn diagram to give all situations for cutting wires to defuse the bombs. So I had spoilers to this.
That was my first thought, too. They only really work properly through 4, but they're so nice when they do. (After 4, you either need more than three dimensions or not all related regions are adjacent.)
I'm glad finally someone had the courage to speak the truth
😂😂😂
This is a really good video!
Interesting how normal Venn diagrams lack the 2 extra spaces.
However, I do think that normal 4 circle Venn diagrams are good in some situations.
For example, I saw a 4 circle Venn diagram which compares stimulants, depressants, hallucinogens, and anti psychotics. Since stimulants and depressants are opposites, comparing them is not possible. Same goes for the other 2. I think that in rare cases like these where those 2 missing spaces work in favor of the context, it is good.
Otherwise, your Peyam diagram is super neat!
Dr. Peyam said you can do this with spheres.
That generalizes.
For 2 sets, you can use 2 segments.
For 3 sets, use 3 circles.
For 4 sets, use 4 spheres.
For n sets, use n "spheres" of S_n-2.
All you need is an n-1 dimensional board to draw on.
😜
I'd love to have a 420 dimensional :(
You opened a great thing which most of us missed to experiment in our school days.. made it so clear Doctor.. thanks a lot for that.. 😊😊👍
What is the highest number you can do with just ellipses? The wikipedia article has a 5 one but is that the highest? Or can you do any number but they get hard to find?
Or is it just that with blobs you can just keep adding but with ellipses you have to redraw?
Dr peyam is best
I see something weird...
Starting from set C, a circle; set D, a dumbbell; set E, a cross...They just look like the electron orbitals s, p, d. Is that anything relevant or just a coincidence?
Elections do jump from one orbital to another, so there might be some sort of "stair areas"?🤔
Edit: elevator areas?
Interesting 🤔
im leaning on something relevant
@@drpeyam Following the line of thinking, what are sets A and B represent if the diagram is really related to electron orbitals, which by themselves are indeed probabilistic functions?
Set a,b&c are all symmetric
"Snarky Math" had a video on this last week. Great minds think alike, maybe you two should collaborate some time.
Very clear. Thank you.
@Dr Peyam I have a question which I dunno how to solve
[q(x)]² = 9x⁴ + kx³ + lx² - 4x + 4
To find : value of (k+l)
A little hint how to approach would be enough...
Assuming q(x) is a polynomial, we can assume q(x) to be 3x^2 + cx +2 , can you see how squaring it leads to getting constant term of 4 and leading coefficient as 9, now expand it and compare it with the given equation.
Here i have taken c as a variable, now when you expand and compare, you should be able to get c=-1
9x^4 + 6c x^3 + (12+c)x^2 + 4cx + 4
@@akshatjangra4167 Thank you very much!
Correct me if I'm wrong:
We get c= -1 by comparing 4cx and -4x in the equation, isn't it?
@@mathenthusiast1729 you are welcome #mathematics4life
After being cordially invited to consult the Venn Diagram wikipedia page, I remarked that although both the French and the English version of this article mention the existence of Smith's equivalent diagrams of the form y_i = sin(2^i x)/2^i, the French one lists this information as questionnable. When further looking at it, the reference is indirect which makes it hard to verify. Do you have some info whether that's true or not?
Also, the Italian and the German one do NOT mention this info and the German one has nice info regarding Venn diagrams and syllogisms.
A second remark, the German article made me think that it is possible that what we are taught is more of a Euler-Diagramme in the German sense as it is a "Venn Diagram but it does not have to have all possibilities of intersection represented".
That’s so interesting! I didn’t know there’s a difference between the wiki pages. I generally think that the English one is most accurate, but maybe I’m wrong. Thanks for checking
@@drpeyam There is indeed a lot of differences between languages in Wikipedia. However, they often don't contradict each other but they often explore a problem in different ways. I often check English/French, sometimes German but I am not fluent in it. I had a discussion with it recently regarding the Wikipedia articles for similarity in geometry (similitude) and they are both fairly different in structure.
In this case, the problem is different because one of the proof is flagged as questionnable in a language, not questionnable in English and not present in others which is rare. Personally, I do not have enough knowledge to assert whether or not Smith's equivalent diagrams works or not. What do you think about it? Is the source trustworthy?
cross-referencing different language versions is one of the big life-hacks to improve the quality of information you get out of wikipedia i reckon
Nice! I guessed the answer was ellipses correctly!!! Heck only real talented people can draw a circle without there being any eccentricity at all and I'm not certainly one of them so it makes sense the answer should be the more natural occurring as opposed to perfect shape.. Dr Peyam what is your favorite Non Euclidean geometry?
Merci !
Many people are commenting on the sets and stuff but the thing to really think about is how is he drawing so neatly
I cut out the parts where I drew it badly haha
I really thought that this would be the dual problem to the problem to find a fully connected planar graph of n nodes :/
The what of what of what?
What do you mean by fully connected? A complete graph? Unlikely to be connected to it anyway since they overlap.
Would have loved a graph theory connection though since that's in my top 3 branches of maths.
You certainly could do a graph with coloured paths where each is one case (single ones can be a loop)
Completed planar graph, sorry. In that problem its only possible for n
Knew you were gonna say elipses! 😅
Great stuff!
But why to get 16
Forgive me, but who said that sets are represented only with circles in Venn diagrams? In Venn diagrams, any closed form can be used to represent a set.
I had played the game "Keep Talking and Nobody Explodes and in the free to access webpage necessary to play the game it shows you a 4 ellipse Venn diagram to give all situations for cutting wires to defuse the bombs. So I had spoilers to this.
interestingly enough, in 3d, using spheres, we can "draw" a symmetrical Venn diagram for 4 sets
Greetings from Chile!
😍 perfect truth for once...
سهل و ممتنع
I saw this problem in snarky math
3:13 AMOGUS
A Peyam diagram. I like it.
Just realised - you’re trying to give each Letter its own unique shape - maybe that’s the key?
Peyam diagram? Peyagram!
The blob shape looks like a Cassini oval.
I prefer Peyam diagram than Venn diagram
Obviously Peyam diagrams >> Venn diagrams
Uups, Venn diagrams should be drawn by Van Gogh....not by mathematicians. :-)
Ellipses can get in the bin. All the cool kids are using Randolph Diagrams 😎
Karnaugh maps
That was my first thought, too. They only really work properly through 4, but they're so nice when they do. (After 4, you either need more than three dimensions or not all related regions are adjacent.)
ENGINEERING entrance Exam
F
F
F
F
I will leave my F for poorly drawn diagram jajaja
F
F
F
F