Introduction to famous curves :-
Rose curve

I thought it a good idea if i posted this topic each week maybe , I'll choose a famous cool curve each time to talk about, ready to answer any question about it, just feel free to ask and maybe share cool ideas :)
i hope you to have fun with it !

Question

Introduction to famous  curves :-
Rose curve

I thought it a good idea if i posted this topic  each week maybe , I'll choose a famous cool curve each time to talk about, ready to answer any question about it, just feel free to ask and maybe share cool ideas :)
i hope you to have fun with it !

anonymous · Answer

A curve which has the shape of a petalled flower. This curve was named rhodonea by the Italian mathematician Guido Grandi between 1723 and 1728 because it resembles a rose (MacTutor Archive). The polar equation of the rose is

 $r=a\sin(n\theta)$ 
or

 $r=acos(n\theta)$.

anonymous · Answer

I'll start with $r=a\sin(n\theta)$ $a$ affects on expanding and sketching i'll show you n effects only when $n$ is $0$ the graph is a point $ \sin 0=0$ . case 1:- the standard graph when $n=1$ http://prntscr.com/5vq2z2 case 2:- when $|n|<1$ note when its negative the its reflective around $x$ axis so when $n=1/m$ and $m$ is even no change happens . http://prntscr.com/5vq3xu when $n=1/m$ and $m$ is odd http://prntscr.com/5vq88v case 3:- when $|n|>1$ the graph would be just like petal and u'll note $n$ is the petals numbers , when $n$ is negative odd is a reflexive of the graph when $n$ is positive around $x$ axis http://prntscr.com/5vqfi7 when $n$ is even then the number of petals is $2n$ http://prntscr.com/5vqke2 FOR MORE FUN https://www.desmos.com/calculator/tyuk4he0e3

anonymous · Answer

i'll continue on this later since i dint add the spiral case when n is too small

ganeshie8 · Answer

that desmos link is amazing xD

anonymous · Answer

haha yeah

kainui · Answer

https://www.desmos.com/calculator/n5ussfeanz

nnesha · Answer

hmm waoo thatz cool ^^^^^^looks amazing

anonymous · Answer

aww that so nice :O