File:Arc length, Fermat.svg
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Summary
editDescriptionArc length, Fermat.svg |
English: This graph is meant to help accompany the article Length of an arc and describe the method Fermat used.
Español: Ilustración del método de Fermat para calcular la longitud de arco de una curva. |
Date | |
Source | Own work |
Author | Nicoguaro |
SVG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
rcParams['font.size'] = 16
fun = lambda x: x**1.5
tangent = lambda x, a: 1.5*a**0.5*(x - a) + a**1.5
a = 0.6
e = 0.45*a
lo = e/10 # Offset of annotations
# Principal plots
x = np.linspace(0, 1.2, 100)
y1 = fun(x)
y2 = tangent(x, a)
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(1, 1, 1)
plt.plot(x, y1, "r", lw=2)
plt.plot(x[y2>=0], y2[y2>=0], "k", lw=2)
# Auxiliar lines
plt.plot([0, 1.2], [fun(a), fun(a)], "--k", lw=1, alpha=0.5)
plt.plot([a, a], [0, y2[-1]], "--k", lw=1, alpha=0.5)
plt.plot([a + e, a + e], [0, y2[-1]], "--k", lw=1, alpha=0.5)
# Intersections points
plt.plot(a, fun(a), 'rs')
plt.annotate("A", xy=(a, fun(a) + lo))
plt.plot(a + e, fun(a), 'rs')
plt.annotate("B", xy=(a + e + lo, fun(a) + lo))
plt.plot(a + e, tangent(a+e, a), 'rs')
plt.annotate("C", xy=(a + e + lo, tangent(a+e, a) - lo))
plt.plot(a + e, fun(a+e), 'rs')
plt.annotate("D", xy=(a + e - lo, fun(a+e) + lo))
# Functions labels
plt.annotate(r"$y=x^{3/2}$", xy=(0.2, 0.2))
plt.annotate(r"$y=\frac{3\sqrt{a}}{2} (x - a) + a^{3/2}$", xy=(0.35, 0.12))
plt.xlim([0, 1.2])
plt.ylim([0, 2.5*fun(a)])
plt.xticks([a, a+e], [r"$a$", r"$a + e$"])
plt.yticks([fun(a)], [r"$a^{3/2}$"])
plt.savefig("Arc length, Fermat.svg", bbox_inches="tight")
plt.show()
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Licensing
editI, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:42, 12 February 2016 | 615 × 618 (26 KB) | Nicoguaro (talk | contribs) | Fit lines inside the plotting box and change some colors. | |
16:33, 12 February 2016 | 615 × 618 (25 KB) | Nicoguaro (talk | contribs) | User created page with UploadWizard |
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Width | 492pt |
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Height | 494pt |