Let the circle radius of Taiji diagram be 6 and the angle unit be radian. In terms of symmetry, we only need to study the summer solstice-the autumnal equinox-the winter solstice.
It is easy to find out that the Taiji curve can be expressed as ρ=﹙6/π﹚×﹙θ+π/2﹚[ for example, θ = π/6 ﹚ = 4] in polar coordinates.
Let's calculate the area ratio of Yin and Yang in Qi Festival from summer to Millennium. Total area = π× 6? /24=3π/2
Poplar area = ∫ [π/ 12, π/6]- 1/2-ρ? dθ=6θ? /π? -9θ? [π/ 12, π/6] = 9π/32 /π+9θ/2.
Yin area = 3 π/2-9 π/32 = 39 π/32 Yang area/Yin area = 9/39.