File:Arc length, Fermat.svg
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Size of this PNG preview of this SVG file: 597 × 600 pixels. Other resolutions: 239 × 240 pixels | 478 × 480 pixels | 764 × 768 pixels | 1,019 × 1,024 pixels | 2,038 × 2,048 pixels | 615 × 618 pixels.
Original file (SVG file, nominally 615 × 618 pixels, file size: 26 KB)
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Summary
[edit]DescriptionArc 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()
|
Licensing
[edit]I, 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.
File history
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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 |
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12 February 2016
image/svg+xml
e7ae0e4eb88be7b0e8c1ee9285ea8c5ab21725f6
27,134 byte
618 pixel
615 pixel
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