算額（その33）
岩手県一関市 八幡神社 天保9年(1838)
http://www.wasan.jp/iwate/itinosekiyahata2.html
円の中に 4 種類の円が収まっている。各円の径を求めよ。
算額の図では中央にある円と上下端にある円は違う色で塗られているが，これは同じ径を持つ円でなければ計算が合わない。
using SymPy
@syms r1::positive, r2::positive, r3::positive, r4::positive, x4::positive;
eq1 = x4^2 + r4^2 - (r3 + r4)^2;
eq2 = x4^2 + (r4 - r1 - r3)^2 - (r1 + r4)^2;
eq3 = r3 + 2r1 + 2r2 - 1;
eq4 = 1 - 2r4 - r3;
eq5 = r2 - r3;
solve([eq1, eq2, eq3, eq4, eq5], (r1, r2, r3, r4, x4))
1-element Vector{NTuple{5, Sym}}:
(1/8, 1/4, 1/4, 3/8, 1/2)
using Plots
function circle(ox, oy, r, color=:red; beginangle=0, endangle=360)
θ = beginangle:0.1:endangle
x = r.*cosd.(θ)
y = r.*sind.(θ)
plot!(ox .+ x, oy .+ y, color=color, linewidth=0.5)
end;
function point(x, y, string="", color=:green, position=:left, vertical=:top)
scatter!([x], [y], color=color, markerstrokewidth=0)
annotate!(x, y, text(string, 10, position, color, vertical))
end;
function draw(more=false)
pyplot(size=(500, 500), grid=false, aspectratio=1, label="", fontfamily="IPAMincho")
r1, r2, r3, r4, x4 = (1/8, 1/4, 1/4, 3/8, 1/2)
println("r1 = $r1; r2 = $r2; r3 = $r3; r4 = $r4")
println("x4= $x4")
plot()
circle(0, 0, r3, :green)
circle(0, r1+r3, r1, :blue)
circle(0, -r1-r3, r1, :blue)
circle(0, r3 + 2r1 + r2, r2, :red)
circle(0, -r3 - 2r1 - r2, r2, :red)
circle(x4, r4, r4, :magenta)
circle(x4, -r4, r4, :magenta)
circle(-x4, r4, r4, :magenta)
circle(-x4, -r4, r4, :magenta)
if more
point(0, 0, "0 ", :black, :right)
point(0, r3, "r3 ", :black, :right)
point(0, r3+r1, "r3+r1 ", :blue, :right)
point(0, 1-r2, "1-r2 ", :red, :right)
point(x4, r4, "(x4,r4)", :magenta, :center)
vline!([0], color=:black, linewidth=0.25)
hline!([0], color=:black, linewidth=0.25)
end
circle(0, 0, 1, :black)
end;
