04/12/2023 1

The equations have been derived by the author.These curves are drawn using Matlab.

Each curve represents a family of curves.The equations follow the curves.For the theory, you may look for

‘Functional Theoretic Algebra’ and ‘n-curve’ in Wikipedia.

Sebastian Vattamattam

Beautiful Mathematical Curves

204/12/202340

10

]2sin2[sin44cos

]2cos2[cos44

n

t

tntty

tnttx

),( with curved-n Curve Cosine The uun

304/12/2023

3cos curve Rhodonea with thecurved-n Curve Cosine The

15

10

2sin.6cos22cos

]2cos.6cos1[2

n

t

ntntty

ntnttx

404/12/2023

Folium Double theis Here . form theof CurveA n

4010

2sin2cos42sin2cos44sin4sin

33

22

nt

ttntntyntntx

504/12/2023

),(u with curved-n Spiraln Archimedea The n u

10]2sin2[sin22sin2]2cos2[cos22cos2

ttntttytntttx

604/12/2023

),(u with curved-n LinsegmentA n u

4010

2sin2cos2sin2cos2sin2cos2sin2cos

nt

ttntnttyttntnttx

704/12/2023

Folium Double with theCurved-n curve Cosine The

6010

2sin2sin12cos2cos

3

3

nt

nttynttx

804/12/2023

Circle Unit theand 2cos Curve Rhodonea theofProduct f

7010

2sin2sin.4cos12cos2cos.4cos

nt

ntttyntttx

904/12/2023

circle-n theand Astroid theofProduct -f

6010

2sin2sin12cos2cos

3

3

nt

nttynttx

1004/12/2023

nm u circle-n and u circle-m ofProduct -f

2,1010

2cos.

2sin2

12

cos.2

cos2

nmt

tnm

tnm

y

tnm

tnm

x

1104/12/2023

nm u circle-n and u circle-m ofProduct -f

4,1610

2cos.

2sin2

12

cos.2

cos2

nmt

tnm

tnm

y

tnm

tnm

x