新地図投影法は数学的発見ですよね。
ネットを探す限り前例がないようなので、 #村上無特異点正積図法 #Murakami no singular point equal-area Projectionと主張しておきます。
var('l p')
s=1.3321239939739768
x(l,p)=s^2*cos(p+(s-1)/(2*(s+1))*sin(2*p))*sin(l*(2/(s+1))^2*cos(p)/(cos(p+(s-1)/(2*(s+1))*sin(2*p))*(1+(s-1)/(s+1)*cos(2*p))))/(cos(p+(s-1)/(2*(s+1))*sin(2*p))*cos(l*(2/(s+1))^2*cos(p)/(cos(p+(s-1)/(2*(s+1))*sin(2*p))*(1+(s-1)/(s+1)*cos(2*p))))+1)^0.5
y(l,p)=sin(p+(s-1)/(2*(s+1))*sin(2*p))/(cos(p+(s-1)/(2*(s+1))*sin(2*p))*cos(l*(2/(s+1))^2*cos(p)/(cos(p+(s-1)/(2*(s+1))*sin(2*p))*(1+(s-1)/(s+1)*cos(2*p))))+1)^0.5
l1=parametric_plot((x(-pi,p),y(-pi,p)),(p,-pi/2,pi/2))
l2=parametric_plot((x(-pi*5/6,p),y(-pi*5/6,p)),(p,-pi/2,pi/2))
l3=parametric_plot((x(-pi*4/6,p),y(-pi*4/6,p)),(p,-pi/2,pi/2))
l4=parametric_plot((x(-pi*3/6,p),y(-pi*3/6,p)),(p,-pi/2,pi/2))
l5=parametric_plot((x(-pi*2/6,p),y(-pi*2/6,p)),(p,-pi/2,pi/2))
l6=parametric_plot((x(-pi*1/6,p),y(-pi*1/6,p)),(p,-pi/2,pi/2))
l17=parametric_plot((x(pi*0.001/6,p),y(pi*0.001/6,p)),(p,-pi/2,pi/2))
l7=parametric_plot((x(pi*1/6,p),y(pi*1/6,p)),(p,-pi/2,pi/2))
l8=parametric_plot((x(pi*2/6,p),y(pi*2/6,p)),(p,-pi/2,pi/2))
l9=parametric_plot((x(pi*3/6,p),y(pi*3/6,p)),(p,-pi/2,pi/2))
l10=parametric_plot((x(pi*4/6,p),y(pi*4/6,p)),(p,-pi/2,pi/2))
l11=parametric_plot((x(pi*5/6,p),y(pi*5/6,p)),(p,-pi/2,pi/2))
l12=parametric_plot((x(pi,p),y(pi,p)),(p,-pi/2,pi/2))
l13=parametric_plot((x(l,-pi*2/6),y(l,-pi*2/6)),(l,-pi,pi))
l14=parametric_plot((x(l,-pi*1/6),y(l,-pi*1/6)),(l,-pi,pi))
l18=parametric_plot((x(l,pi*0.001/6),y(l,pi*0.001/6)),(l,-pi,pi))
l15=parametric_plot((x(l,pi*1/6),y(l,pi*1/6)),(l,-pi,pi))
l16=parametric_plot((x(l,pi*2/6),y(l,pi*2/6)),(l,-pi,pi))
show(l1+l2+l3+l4+l5+l6+l7+l8+l9+l10+l11+l12+l13+l14+l15+l16+l17+l18,figsize=4.5,xmin=x(-pi,0),xmax=x(pi,0),ymin=x(-pi,0),ymax=x(pi,0),axes=false)