The posted coordinates is useless.
I'm interested in calculation, graphic design and geocaching!
This semester I learned polor coordinates in college.
With some equations,you can create many unique patterns on paper.
The first equation I learned is r = 1 + sinθ.
I was amazed by the answer:
The pattern is called "cardioid".What a miracle in Mathimatics!
Then,I found lots of spirals,waves and curves on my textbook.
Just changing times in trigonometric function,which is like
r = sin3θ
r = cos4θ
or r = sinθ + 2sin2θ
Then these patterns will become many beautiful types.
When the professor explained this equation:
r = sin3θ + 0.3sin9θ
"Wow! A Clover!"
"But Lucky clover should be 4-leaf!"
So,I started to find where was my 4-leaf clover.
After several attempts , I did it!
The equation is r = sin2θ + 0.3sin6θ
Let's draw a small part of it's pattern:
If 0 ≦ θ ≦ π/12 , 0 ≦ 2θ ≦ π/6 , 0 ≦ 6θ ≦ π/2,
then 0 ≦ sin2θ ≦ 1/2 , 0 ≦ 0.3sin6θ ≦ 0.3,
so 0 ≦ r ≦ 0.8 ,when 0 ≦ θ ≦ π/12
If we see the graph three equation r = sin2θ + 0.3sin6θ , r=0.8 , θ = π/12
have an intersection(red circle)
Connect origin with the crossover point ,find a appropriate radian (thick red line)
yep , we drew a small section of the pattern of r = sin2θ + 0.3sin6θ
Now all we have to do is finish the remaining graph : π/12 ≦ θ ≦ 2π.
We'll get the anwser!
Now it's your turn!
Believe the answer is always in your heart.
It would be easier if you use the website to browse description
You can validate your puzzle solution with certitude.