Akiva Weinberger
@akivaw.bsky.social
Likes math. Asleep when you least expect it. His origins and motivations remain unclear.
October 20, 2025 at 9:57 PM
Proof that pi is irrational:
Consider the following table.
If pi=A/B, the values are an integer multiple of 1/B^n, but they tend to zero super-exponentially.
QED
(Actually this shows that pi^2 is irrational)
Consider the following table.
If pi=A/B, the values are an integer multiple of 1/B^n, but they tend to zero super-exponentially.
QED
(Actually this shows that pi^2 is irrational)
September 18, 2025 at 7:47 PM
Proof that pi is irrational:
Consider the following table.
If pi=A/B, the values are an integer multiple of 1/B^n, but they tend to zero super-exponentially.
QED
(Actually this shows that pi^2 is irrational)
Consider the following table.
If pi=A/B, the values are an integer multiple of 1/B^n, but they tend to zero super-exponentially.
QED
(Actually this shows that pi^2 is irrational)
I have not seen this film but these two people are playing eyeball
August 18, 2025 at 2:23 PM
I have not seen this film but these two people are playing eyeball
Someone else can execute on this vision way better than I can
August 3, 2025 at 6:17 PM
Someone else can execute on this vision way better than I can
The best elaboration on "season to taste" I've ever seen
July 8, 2025 at 3:03 PM
The best elaboration on "season to taste" I've ever seen
Noticed something interesting looking at a map of light pollution. What's this dot in the middle of the Teklimakan Desert, China? Is it a military outpost?
July 1, 2025 at 1:52 AM
Noticed something interesting looking at a map of light pollution. What's this dot in the middle of the Teklimakan Desert, China? Is it a military outpost?
Why does Charlotte, NC look like it has a budget version of the Shanghai World Financial Center
May 27, 2025 at 9:20 PM
Why does Charlotte, NC look like it has a budget version of the Shanghai World Financial Center
Surprised nobody's drawn this picture yet.
(I guess it's a little sloppy to use dx instead of Δx.)
(I guess it's a little sloppy to use dx instead of Δx.)
May 4, 2025 at 4:18 AM
Surprised nobody's drawn this picture yet.
(I guess it's a little sloppy to use dx instead of Δx.)
(I guess it's a little sloppy to use dx instead of Δx.)
Here's the problem: Find the angle α in the figure below.
It's a simple angle chase… or is it?
It's a simple angle chase… or is it?
March 12, 2025 at 12:06 AM
Here's the problem: Find the angle α in the figure below.
It's a simple angle chase… or is it?
It's a simple angle chase… or is it?
Interesting. No idea why this would be the case
March 2, 2025 at 4:29 AM
Interesting. No idea why this would be the case
It's a neat exercise to do a similar thing for x/(1-x-x^2), in the regions |x|<0.618, 0.618<|x|<1.618, and 1.618<|x|. (The second series is doubly infinite.)
January 3, 2025 at 8:17 AM
It's a neat exercise to do a similar thing for x/(1-x-x^2), in the regions |x|<0.618, 0.618<|x|<1.618, and 1.618<|x|. (The second series is doubly infinite.)
This is related to how the function
1/(1-x)
can be written as a power series in two different ways:
1+x+x^2+x^3+… (when |x|<1)
-x^(-1)-x^(-2)-x^(-3)-… (when |x|>1)
Ignoring the domains of convergence, subtracting the two leads to the "conclusion" that
…+x^(-2)+x^(-1)+1+x+x^2+… = 0.
1/(1-x)
can be written as a power series in two different ways:
1+x+x^2+x^3+… (when |x|<1)
-x^(-1)-x^(-2)-x^(-3)-… (when |x|>1)
Ignoring the domains of convergence, subtracting the two leads to the "conclusion" that
…+x^(-2)+x^(-1)+1+x+x^2+… = 0.
January 3, 2025 at 8:15 AM
This is related to how the function
1/(1-x)
can be written as a power series in two different ways:
1+x+x^2+x^3+… (when |x|<1)
-x^(-1)-x^(-2)-x^(-3)-… (when |x|>1)
Ignoring the domains of convergence, subtracting the two leads to the "conclusion" that
…+x^(-2)+x^(-1)+1+x+x^2+… = 0.
1/(1-x)
can be written as a power series in two different ways:
1+x+x^2+x^3+… (when |x|<1)
-x^(-1)-x^(-2)-x^(-3)-… (when |x|>1)
Ignoring the domains of convergence, subtracting the two leads to the "conclusion" that
…+x^(-2)+x^(-1)+1+x+x^2+… = 0.
And see here for some nicer-looking solutions to the same problem. I'll leave these a mystery for now…
December 24, 2024 at 9:59 PM
And see here for some nicer-looking solutions to the same problem. I'll leave these a mystery for now…
Here's a function whose zeros are precisely 1 and the primes.
The first term checks for primarily uses Wilson's theorem (en.wikipedia.org/wiki/Wilson%...); the second term checks that it's an integer.
The first term checks for primarily uses Wilson's theorem (en.wikipedia.org/wiki/Wilson%...); the second term checks that it's an integer.
December 24, 2024 at 9:59 PM
Here's a function whose zeros are precisely 1 and the primes.
The first term checks for primarily uses Wilson's theorem (en.wikipedia.org/wiki/Wilson%...); the second term checks that it's an integer.
The first term checks for primarily uses Wilson's theorem (en.wikipedia.org/wiki/Wilson%...); the second term checks that it's an integer.
I feel like I owe you an actual chart after all this.
There are only 2 connected graphs with three vertices (a line and a triangle). There are 6 with four vertices, and 21 with five vertices. There are over a 11 million with ten vertices. How quickly does this grow?
Here's a log graph, up to 50.
There are only 2 connected graphs with three vertices (a line and a triangle). There are 6 with four vertices, and 21 with five vertices. There are over a 11 million with ten vertices. How quickly does this grow?
Here's a log graph, up to 50.
December 12, 2024 at 1:10 AM
I feel like I owe you an actual chart after all this.
There are only 2 connected graphs with three vertices (a line and a triangle). There are 6 with four vertices, and 21 with five vertices. There are over a 11 million with ten vertices. How quickly does this grow?
Here's a log graph, up to 50.
There are only 2 connected graphs with three vertices (a line and a triangle). There are 6 with four vertices, and 21 with five vertices. There are over a 11 million with ten vertices. How quickly does this grow?
Here's a log graph, up to 50.
At the risk of bringing up politics, I want to share this PragerU graph. It's "good" at being a hilariously awful graph.
Completely made-up data (what metric is "standards" measured in? What are the units?) Probably created to give the illusion of scientific rigor to a gullible audience.
Completely made-up data (what metric is "standards" measured in? What are the units?) Probably created to give the illusion of scientific rigor to a gullible audience.
December 12, 2024 at 12:44 AM
At the risk of bringing up politics, I want to share this PragerU graph. It's "good" at being a hilariously awful graph.
Completely made-up data (what metric is "standards" measured in? What are the units?) Probably created to give the illusion of scientific rigor to a gullible audience.
Completely made-up data (what metric is "standards" measured in? What are the units?) Probably created to give the illusion of scientific rigor to a gullible audience.
Another thing graph theorists like to do is coloring graphs: giving the vertices colors so that no two vertices share the same color. We might ask questions like, "For this graph, how many colors are necessary"?
December 12, 2024 at 12:38 AM
Another thing graph theorists like to do is coloring graphs: giving the vertices colors so that no two vertices share the same color. We might ask questions like, "For this graph, how many colors are necessary"?
You should specify what kind of "graph" you mean!
December 12, 2024 at 12:38 AM
You should specify what kind of "graph" you mean!
No one's built a life-size sofa and corridor demonstration of the moving sofa problem. Who do I call to fix this
December 11, 2024 at 11:38 PM
No one's built a life-size sofa and corridor demonstration of the moving sofa problem. Who do I call to fix this
The symbol is from the flag of Chicago.
December 11, 2024 at 5:25 PM
The symbol is from the flag of Chicago.
Of course, nothing can beat the flag of Pskov, Russia, in which God pets a cat
December 11, 2024 at 5:19 PM
Of course, nothing can beat the flag of Pskov, Russia, in which God pets a cat
The middle one is pretty close to the Chicago flag, which is probably a bonus
December 11, 2024 at 5:18 PM
The middle one is pretty close to the Chicago flag, which is probably a bonus