The rose curve develops a formula 𝑟 = 𝑎 𝑐𝑜𝑠 (𝑛θ) that can draw flowers with different numbers of pedals. By changing the value of n, the number of pedals will change. if the number of n is an irrational number, the shape will be unbounded and infinite.
The 3D equation of a heart develops from the 2D equation of a heart curve (x^2 + y^2 – 1)^3 – x^2 y^3 = 0. By integrating the terms of z into it, the equation becomes: (x^2 + y^2 + z^2 – 1)^3 – x^2 z^3 – y^2 z^3 = 0. Then, from the original turnip shape produced by using the foundational function developed from 2D heart curve, a perfect 3D heart could be adjusted and produced by changing the coefficients of each term of the equation.
