2023-09-08

In [1]:

import numpy as np
import matplotlib.pyplot as plt

import numpy as np import matplotlib.pyplot as plt

In [2]:

n = np.arange(250, 2000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

n = np.arange(250, 2000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1)

Out[2]:

<matplotlib.collections.PathCollection at 0x7f95691bee20>

In [3]:

n = np.arange(250, 2000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

for m in range(250, 2000):
    lowest_distance = 10
    lowest_distance_n = 0

    for n in range(250, 2000):
        if m == n:
            continue
        distance = np.sqrt((1/n - 1/m)**2 * 10 ** 6 + (np.sin(n) - np.sin(m))**2)
        if distance < lowest_distance:
            lowest_distance = distance
            lowest_distance_n = n

    # print(m, lowest_distance_n)
    # plot line between (1/m, sin(m)) and (1/n, sin(n))
    plt.plot([1/m, 1/lowest_distance_n], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08)

plt.savefig('images/20230908-01.png', dpi=300)

n = np.arange(250, 2000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1) for m in range(250, 2000): lowest_distance = 10 lowest_distance_n = 0 for n in range(250, 2000): if m == n: continue distance = np.sqrt((1/n - 1/m)**2 * 10 ** 6 + (np.sin(n) - np.sin(m))**2) if distance < lowest_distance: lowest_distance = distance lowest_distance_n = n # print(m, lowest_distance_n) # plot line between (1/m, sin(m)) and (1/n, sin(n)) plt.plot([1/m, 1/lowest_distance_n], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08) plt.savefig('images/20230908-01.png', dpi=300)

In [14]:

x = np.arange(1e-6, 1, 0.001)
y = np.sin(1/x)

plt.plot(x,y)

x = np.arange(1e-6, 1, 0.001) y = np.sin(1/x) plt.plot(x,y)

Out[14]:

[<matplotlib.lines.Line2D at 0x7f95608e18b0>]

In [42]:

n = np.arange(2000, 20000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

n = np.arange(2000, 20000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1)

Out[42]:

<matplotlib.collections.PathCollection at 0x7f9560014d60>

In [30]:

n = np.arange(2000, 20000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

n = np.arange(1, 2000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

n = np.arange(2000, 20000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1) n = np.arange(1, 2000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1)

Out[30]:

<matplotlib.collections.PathCollection at 0x7f95680f9f40>

In [31]:

n = np.arange(1, 2000, 1)
x = np.log(1/n)
y = np.sin(n)

plt.scatter(x, y, s=1)

n = np.arange(1, 2000, 1) x = np.log(1/n) y = np.sin(n) plt.scatter(x, y, s=1)

Out[31]:

<matplotlib.collections.PathCollection at 0x7f956136d130>

In [29]:

n = np.arange(250, 2000, 1)
x = np.log(1/n)
y = np.sin(n)

plt.scatter(x, y, s=1)

for m in range(250, 2000):
    lowest_distance = 10
    lowest_distance_n = 0

    for n in range(250, 2000):
        if m == n:
            continue
        distance = np.sqrt((np.log(1/n) - np.log(1/m))**2 + (np.sin(n) - np.sin(m))**2)
        if distance < lowest_distance:
            lowest_distance = distance
            lowest_distance_n = n

    # print(m, lowest_distance_n)
    # plot line between (1/m, sin(m)) and (1/n, sin(n))
    plt.plot([np.log(1/m), np.log(1/lowest_distance_n)], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08)

plt.savefig('images/20230908-02.png', dpi=300)

n = np.arange(250, 2000, 1) x = np.log(1/n) y = np.sin(n) plt.scatter(x, y, s=1) for m in range(250, 2000): lowest_distance = 10 lowest_distance_n = 0 for n in range(250, 2000): if m == n: continue distance = np.sqrt((np.log(1/n) - np.log(1/m))**2 + (np.sin(n) - np.sin(m))**2) if distance < lowest_distance: lowest_distance = distance lowest_distance_n = n # print(m, lowest_distance_n) # plot line between (1/m, sin(m)) and (1/n, sin(n)) plt.plot([np.log(1/m), np.log(1/lowest_distance_n)], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08) plt.savefig('images/20230908-02.png', dpi=300)

KeyboardInterrupt

In [22]:

n = np.arange(250, 2000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

for m in range(250, 2000):
    lowest_distance = 10
    lowest_distance_n = 0

    for n in range(250, 2000):
        if m == n:
            continue
        distance = np.sqrt((1/n - 1/m)**2 + (np.sin(n) - np.sin(m))**2)
        if distance < lowest_distance:
            lowest_distance = distance
            lowest_distance_n = n

    # print(m, lowest_distance_n)
    # plot line between (1/m, sin(m)) and (1/n, sin(n))
    plt.plot([1/m, 1/lowest_distance_n], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08)

plt.savefig('images/20230908-03.png', dpi=300)

n = np.arange(250, 2000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1) for m in range(250, 2000): lowest_distance = 10 lowest_distance_n = 0 for n in range(250, 2000): if m == n: continue distance = np.sqrt((1/n - 1/m)**2 + (np.sin(n) - np.sin(m))**2) if distance < lowest_distance: lowest_distance = distance lowest_distance_n = n # print(m, lowest_distance_n) # plot line between (1/m, sin(m)) and (1/n, sin(n)) plt.plot([1/m, 1/lowest_distance_n], [np.sin(m), np.sin(lowest_distance_n)], color='red', linewidth=0.08) plt.savefig('images/20230908-03.png', dpi=300)

In [33]:

n = np.arange(250, 2000, 1)
x = 1/n
y = np.sin(n)

plt.scatter(x, y, s=1)

for m in range(250, 2000):
    lowest_distance = 10
    lowest_distance_n = 0
    
    plt.plot([1/m, 1/(m+44)], [np.sin(m), np.sin(m+4)], color='red', linewidth=0.08)

plt.savefig('images/20230908-04.png', dpi=300)

n = np.arange(250, 2000, 1) x = 1/n y = np.sin(n) plt.scatter(x, y, s=1) for m in range(250, 2000): lowest_distance = 10 lowest_distance_n = 0 plt.plot([1/m, 1/(m+44)], [np.sin(m), np.sin(m+4)], color='red', linewidth=0.08) plt.savefig('images/20230908-04.png', dpi=300)

In [38]:

_n = np.arange(250, 2000, 1)
x = 1/_n
y = np.sin(_n)

plt.scatter(x, y, s=1)

for m in _n:
    n = 1

    cs = np.abs(np.where(np.abs(y - np.sin(m)) < 0.001))
    n = np.min(np.abs(cs - m))
    
    
    plt.plot([1/m, 1/(n)], [np.sin(m), np.sin(n)], color='red', linewidth=0.08)

plt.savefig('images/20230908-05.png', dpi=300)

_n = np.arange(250, 2000, 1) x = 1/_n y = np.sin(_n) plt.scatter(x, y, s=1) for m in _n: n = 1 cs = np.abs(np.where(np.abs(y - np.sin(m)) < 0.001)) n = np.min(np.abs(cs - m)) plt.plot([1/m, 1/(n)], [np.sin(m), np.sin(n)], color='red', linewidth=0.08) plt.savefig('images/20230908-05.png', dpi=300)

In [ ]: