Huge thanks to Jane Street! https://www.janestreet.com/join-jane-street/ Check out Ben Sparks’s GeoGebra files. Binet formula 2D complex output: …
source
Copyright (c) 2020 – All rights reserved.
Complex Fibonacci Numbers?
ADVERTISEMENT
6:45 You just made me fell of the chair. Expect the bill from my orthopedist to arrive soon.
Starting points e and pi.
quaternions?
Don't You Only Have To Mirror The Sequence In The Positive Direction And Check It's Position?
Matt Parker: uses Python and Excel to plot 3-D complex values
MATLAB: Am I a joke to you?
GREAT show, as usual.
One problem with visualizing complex numbers with a grid system—and it is something we all do—is that it implies multiples of i have order. It doesn't.
Perhaps the meaning of order and number systems that avoid any semblance of before-after or bigger-smaller, except for the occasional 100% Real intersections could be a future video?
Multidimensional constructs can—and most do—have order. It is possible to determine which of two hyperspheres is larger. Pure complex "shape", it does not even make sense to discuss shape because shape implies size and size comparisons require order.
Limiting our discussion to the absolute value of complex terms avoids the problem—but the absolute values are no longer truly complex, are they?
use quarternions for values of n and get 8-dimensional graphs. 16-dimensional graphs from octonions, and…unfortunately nothing for 6 dimensions, which would be cool because you could have two perpendicular 3D universes.
Go check out the website ‘complex function plotter’
I don't know – somehow I get this remote intuitive feeling that there is a connection between this 4D plot where you can sort of see two layers of 3D wave function and the quantum nature of particles and THEIR wave functions…. or rather that there's something erm… analogous between the nature of i and the time-component of space-time….
I'm a total lay person but I like looking for patterns in allegedly totally unrelated phenomena 🙂
4:50 – how you get the 0th number?
Amazing! Good work!!
Where can you end up? Pi root 2 and the golden ratio pretty much.
Matt just looks so happy, and it makes me happy. This is actually a really cool find! Well done!
I wonder what Binet would say if he saw this video
I wish I had friends that were into stuff like this. Real life isn’t half as interesting as the internet :/
I think you need Matlab, not Excel…
How do you make Excel graphs look fancy?
Your flying fase is verry funny, and also little bit cool. I have never seen that before. ?
This was one of the coolest Fibonacci maths I've ever seen!!!
Wait. I just came from "Brady Numbers" on Numberphile, and 2,308 is the first Brady number. Coincidence?
It got boring afterwards
That was fun to watch
python :
import numpy as np
import matplotlib.pyplot as plt
import scipy.constants
print(scipy.constants.golden)
phi = scipy.constants.golden
def binet(n): # for complex power
#u = phi**n
#v = (1j**2/phi)**n
minus1 = 1j**2
return (phi**n – (minus1/phi)**n)/np.sqrt(5)
for k in range(10):
print(k, int(binet(k).real), binet(k))
#positive numbers
n = np.linspace(0,5,200)
x = binet(n).real
y = binet(n).imag
max_x = int(max(x))
for k in range(max_x+1):
plt.plot(k,0,'b.')
plt.plot(x,y,label='Positive numbers')
#plt.show()
# negative numbers
n = np.linspace(-3,0,200)
x = binet(n).real
y = binet(n).imag
min_x = int(min(x))
for k in range(min_x,0):
plt.plot(k,0,'b.')
plt.plot(x,y, label='Negative numbers')
plt.legend()
plt.grid()
plt.axis('equal')
plt.show()
Codes in Python.
But Matt just loves his spreadsheets.
I loved this video!! THANK YOU!
5:34 that happiness when you allow complex result 🙂
What about considering the quaternion domain?
is this analytic continuation?
Are there any neat graphs about factorials and complex numbers?
6:45 7:24 12:56 18:23
Only a minor Question but isn't it a relation instead of a function?
φ
Hi, I did an animation to display the plot of the Binet formula with the input i component increasing in time. I've uploaded it here. https://youtu.be/mcVtjGT_9fE
There was a Matt Parker who lived in a 4-dimensional shoe…
Cool, but why are you using Excel to draw your plots? Python has some excellent plotting libraries, even before you needed to get Ben’s help.
6:45 Liked and subscribed just for that meme. Good job, Matt 😀
I want your shirt
But, but, can you game the markets with it?
How does he deal with the multiples branches of the fractionnal roots?
That's interesting, if you accomplished that "Amazed Face" bit like I think you did; it's a good visual representation of nontemporal effect for like, three perspectives.
Or the zeroes vis-a-vis the Riemann zeta function?
How does this compare to the gamma function, which also have a bunch of poles in the negative integers.
One way I have seen C -> C functions visualized is with two 2D graphs, one for input and the other for output.
The first graph is a color wheel, and the other is the complex function as a transform of the color wheel. To make it, take the color of position x in the input graph, and plot it at position f(x) in the output graph.
Instead of partially representing 4 perpendicular dimensions in a 3D shape, this represents the function as a transform of a 2D space which we can see entirely.
It would be cool to see this equation in that format. I don't know what this type of graph is called, or if there are prebuilt tools that do this.
You’re getting close to Curious Droid shirt territory, which is a good thing.