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| Description | Ramanujan's construction of an approximate value of . If , then , see Squaring the circle.djvu |
| Date | |
| Source |
Own creation using eukleides and inkscape. The eukleides code is as follows: box(-1, 6, 7, -2)
P = point(0, 2)
R = point(6, 2)
PR = segment(P, R)
draw(PR)
c1 = circle(P, R)
O = center(c1)
draw(c1)
H = barycenter(P, O)
draw(H)
T = barycenter(O, 1, R, 2)
Q0 Q intersection(perpendicular(PR, T), c1)
TQ = segment(T, Q)
draw(TQ)
c2 = circle(R, length(TQ))
S S0 intersection(c1, c2)
RS = segment(R, S)
draw(RS)
PS = segment(P, S)
draw(PS)
N = intersection(parallel(RS, T), line(P, S))
TN = segment(T, N)
draw(TN)
M = intersection(parallel(RS, O), line(P, S))
OM = segment(O, M)
draw(OM)
PM = segment(P, M)
c3 = circle(P, length(PM))
K K0 intersection(c1, c3)
PK = segment(P, K)
draw(PK)
MN = segment(M, N)
c4 = circle(P, length(MN))
L L0 intersection(perpendicular(PR, P), c4)
PL = segment(P, L)
draw(PL)
RL = segment(R, L)
draw(RL)
RK = segment(R, K)
draw(RK)
KL = segment(K, L)
draw(KL)
RH = segment(R, H)
c5 = circle(R, length(RH))
C0 C intersection(line(R, K), c5)
D = intersection(parallel(KL, C), line(R, L))
CD = segment(C, D)
draw(CD)
draw("C", C, 0.1, 315:)
draw("D", D, 0.1, 70:)
draw("H", H, 0.1, 270:)
draw("K", K, 0.1, 250:)
draw("L", L, 0.1, 180:)
draw("M", M, 0.1, 120:)
draw("N", N, 0.1, 120:)
draw("O", O, 0.1, 270:)
draw("P", P, 0.1, 180:)
draw("Q", Q, 0.1, 75:)
draw("R", R, 0.1, 0:)
draw("S", S, 0.1, 30:)
draw("T", T, 0.1, 45:)
|
| Author | GrafZahl |
| Permission (Reusing this file) |
Ineligible for copyright, I believe, because both image and construction are in the public domain. |
|
This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:13, 14 July 2007 | | 720 × 720 (23 KB) | GrafZahl | {{Information |Description=Ramanujan's construction of an approximate value of <math>\sqrt{\pi}</math>. If <math>|OR|=1</math>, then <math>|RD|^2=3.1415929\ldots\approx\pi</math>, see Image:Squaring the circle.djvu |Source=Own creation using [[w:euk |
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