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Richee
BRONZE Member since Jan 2002

HOP librarian
Location: Prague

Total posts: 1841
Posted:-ROSE

-PEDAL CURVE

-NEGATIVE PEDAL CURVE

-SUPERSPIN



---------------------------------------------------------------------------




Non-Https Image Link




ROSE

------------



A curve which has the shape of a petal flower. Curve was named

'Rhodonea' by the Italian mathematician Guido Grandi, between 1723 and 1728 because it resembles a rose.



The polar equation of the rose is":



r = Alfa * sin * (n * Theta) [spin]

r = Alfa * cos * (n * Theta) [anti-spin]



If N is odd, the rose is N-petalled. If N is even, the rose is N-petalled.




Non-Https Image Link




If N is irrational, then there are an infinite number of petals.



N = 2 - Full anti-spin flower.

N = 3 Trifolium(Paquerette de mlibe)

N = 1/2 Half flower.

N = 1/3 Lock-out.

N = 1/5 Snake



Quote:



"If is N = R/S a rational number, then the curve closes at a polar angle

of Theta = PI * S * P ,where P = 1 if R * S is odd and P = 2, if R*S is

even."



Did anyone understand tha last?



PEDAL CURVE

-------------------------



I found that there are flowers divaded into families depending on

origin of the flower, the center.



Trammel(Astroid base) - Full 4 anti-spin flower, with center.

Trimmel(Deltoid base) - Full 3 anti-spin flower, with center.

Hyperbola(Ellipse base) - Circle, with focus(!).

Hypocycloid(Epicycliod base) - Rose(!).

Point(Line base) - Point.




Non-Https Image Link




NEGATIVE PEDAL CURVE

-----------------------------------------



I found, that there is relation between trammel and four fioled

anti-spin. That Trammel is it's, negative pair(!).



That circle negative is elliypse or hyperbola.




Non-Https Image Link




SUPERSPIN

---------------------



It is the ellypse.



---------------------------------------------------------------------------





Source reference:



-Wolfram mathworld(Pedal Curve)

-Trammel

-MacTutor Archive





Thanks math for perfect, math world resource.



Rev, Cole, Mcp, Bluecat*



bending head,



:R


POI THEO(R)IST

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pineapple pete
SILVER Member since Sep 2004

pineapple pete

water based
Location: melbourne

Total posts: 5125
Posted:hmm, interesting.

its still too morning for me to even contemplate how id do that with poi, but ill come back later smile

hug


"you know there are no trophys for doing silly things in real life yeah pete?" said ant "you wont get a 'listened to ride of the valkyries all the way to vietnam' trophy"

*proud owner of the very cute fire_spinning_angel, birgit and neon shaolin*

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NYC


NYC

NYC
Location: NYC, NY, USA

Total posts: 9232
Posted:I used to play with circular graphs on my graphing calculator. You get interesting things in parametrics.

t=sin c x
t=cos c' y

gives interesting patterns when you've got differing rations of c and c'.

I think. If I remembered it correctly. Maybe they were both sin.

Interesting Richee that you've got it in 'polar' form.

With r changing with theta you're essentially changing the length of the string dependant on the angle. Would be tricky but interesting to do in reality.

Unless... you wrapped the strings around each other in some kind of tangled hyper loop. biggrin

You'd get trails like n=1/5 for sure.

You're on to something Richee. Fantastic Geekery. hug


Well, shall we go?
Yes, let's go.
[They do not move.]

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Richee
BRONZE Member since Jan 2002

HOP librarian
Location: Prague

Total posts: 1841
Posted: Written by:

NYC

I think. If I remembered it correctly. Maybe they were both sin.





I think cosinus makes spin, sinus anti-spin,

cause of the curve origin.



huggery,



:R


POI THEO(R)IST

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pineapple pete
SILVER Member since Sep 2004

pineapple pete

water based
Location: melbourne

Total posts: 5125
Posted:nyc, how would you put one of those into a graphics calc?

hug


"you know there are no trophys for doing silly things in real life yeah pete?" said ant "you wont get a 'listened to ride of the valkyries all the way to vietnam' trophy"

*proud owner of the very cute fire_spinning_angel, birgit and neon shaolin*

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87wt2gxq7


87wt2gxq7

veteran
Location: Birmingham

Total posts: 1502
Posted:Richee, what's the origin here - your shoulder or your hand?



Something seems not quite right to me, but it's been a while since I've thought about polar coordinates.



Also,

 Written by: Richee



Code:

r = Alfa * sin (n * Theta)

r = Alfa * cos (n * Theta)







shouldn't that be

Code:

x = Alfa * sin (n * Theta)

y = Alfa * cos (n * Theta)



??



I could be wrong.

Wheee, can't wait till lunchtime to have a good think about this. Will mean I don't get to go outside and spin poi though...


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oli
SILVER Member since Jul 2003

not with cactus
Location: bristol/ southern eastern devo...

Total posts: 2052
Posted: Written by: NYC



With r changing with theta you're essentially changing the length of the string dependant on the angle. Would be tricky but interesting to do in reality.





very good point i think... i mean i like all this maths, but i dont quite see how it can help my poi spinning. i mean there are a two things you can reaistically vary and control when your doing poi, the velocity of your hand and the velocity of the poi head (often changing one affects the other) and changing either affects the path of the poi head.... basically its all boils down to spirographs
and here which makes patterns that are more relevant to poi... i think, or maybe im missing something..


Me train running low on soul coal
They push+pull tactics are driving me loco
They shouldn't do that no no no

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87wt2gxq7


87wt2gxq7

veteran
Location: Birmingham

Total posts: 1502
Posted: Written by: oli


very good point i think... i mean i like all this maths, but i dont quite see how it can help my poi spinning.



I don't see how it can, but it's fun for people who like maths. Is fun not a reason in itself?

It's a bit like the question "what's poi spinning for?" which I usually answer with something pithy like "what's a game of football for?" or (when I'm in a bad mood) "what's a newborn baby for?"

(Incidentally I'm totally ripping that last quote off Faraday - it was his answer to someone who asked him what the use of electricity, which he was performing the first ground-breaking experiments in, was.)


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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay

Total posts: 7330
Posted:oli - you are indeed missing something there...



that page you posted only includes hypotrochoid variants (richee's first set of patterns or 'antispin patterns' as we like to call them).

many of the ones on the page you posted are not possible with poi - the ones without any petals require the poi to be longer than the arm (and probably require them to be solid as well).



the bit that's missing is the fact that there are also epitrichoid variants (richee's rose patterns or 'normal spin'/same-same flowers/lockouts): http://mathworld.wolfram.com/Epitrochoid.html
br>


richee has picked out here those (closed) trochoid patterns that apply specifically to poi patterns.





as an aside, i'll be posting something special here next week that i've waiting for for a while... biggrin ubblove biggrin





cole. x


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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pineapple pete
SILVER Member since Sep 2004

pineapple pete

water based
Location: melbourne

Total posts: 5125
Posted:oooo, very mysterious cole. i look forward too it smile

hug


"you know there are no trophys for doing silly things in real life yeah pete?" said ant "you wont get a 'listened to ride of the valkyries all the way to vietnam' trophy"

*proud owner of the very cute fire_spinning_angel, birgit and neon shaolin*

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oli
SILVER Member since Jul 2003

not with cactus
Location: bristol/ southern eastern devo...

Total posts: 2052
Posted:okay yep, ive thought about it a bit more and i can accept that the patterns richee has posted you probably can do with poi in a reasonable manner, i wasnt convinced before. dose that mean you can get a spirograph to produce richees patterns, specifically the ones with n = 1/5, 2/5 etc...? p.s. i dont see the problem (aside from personal ones) with poi longer than arms...

Me train running low on soul coal
They push+pull tactics are driving me loco
They shouldn't do that no no no

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87wt2gxq7


87wt2gxq7

veteran
Location: Birmingham

Total posts: 1502
Posted: Written by: oli


p.s. i dont see the problem (aside from personal ones) with poi longer than arms...



cept that you could only do the bottom half of longarm moves while standing on a plank suspended above the ground.

Or stilts, yo. biggrin


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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay

Total posts: 7330
Posted:spirographs are a circle rolling around the *inside* of a larger circle - antispin - these are hypotrochoids and are the n>1 patterns that richee posted: http://mathworld.wolfram.com/Hypotrochoid.html
br>


the n<1 trochoids are made by rolling a circle around the *outside* of another circle - normal spin - these are epitrochoids:

http://mathworld.wolfram.com/Epitrochoid.html
br>


so your answer is, if you have a spirographs with cogs on the outside of the big circle, you can make epitrochoid patterns with it smile



as for the 'poi longer than arms' thing, i got that a bit wrong redface

it only determines the size of the petals really.

of the patterns you posted, to spin the ones without petals would require a solid poi (or a club).



having poi that are longer than your arms does make lockout flowers hard to do though cos the poi head will hit the floor when your arm points straight down.

unless you are standing on a pole of course smile



[edit: well in mr 87wt2gxq7!]





cole. x


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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oli
SILVER Member since Jul 2003

not with cactus
Location: bristol/ southern eastern devo...

Total posts: 2052
Posted:right ive thought of something else... i think why i got confused... on a spirograph the rate at which the circle rolls around the other other circle is constant (??), but in order to create some of the patterns richee posted it would have to change... obviusoly this is totally possible with your arms as its not a pice of clock work luckily. but ive got a question... another.. oops, but id like a function that describes the rate that the circle rolls around the other circle... i might try and work it out later or look it up? depends how hard im feeling ubbloco

Me train running low on soul coal
They push+pull tactics are driving me loco
They shouldn't do that no no no

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elasta


elasta

addict
Location: wishing to be in Rio

Total posts: 645
Posted:I'm confused by this part in particular:

[Quote]If N is odd, the rose is N -petalled. If N is even,

the rose is N -petalled. [/Quote]



was that a mistake? what should it have been?

and with the first Rose variant (n=1), is this what you meant Oli where you would have to move the origin of the circle to create that shape? (isolating first upwards then down only on one side yes?)



interesting... but I'm way out of my depth here! keep it up though lads! biggrin


there's nothing quite as fulfilling as a tasty airwrap

if you're full of sh!t, at least you're fertile

"we are all flowers growing in God's garden... and that is why he spreads the sh!t around" - David Byrne

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Posted:Too much math for me. I'm confused and my head hurts.

Too many secerets are locked in side your minds, but your all equal in life, equal in love. your all building castels in the sky dreaming of a better world.

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Glåss
DIAMOND Member since Nov 2001

Glåss

The Ministry of Manipulation
Location: Bristol

Total posts: 2523
Posted:great post, thanks richee biggrin



 Written by: NYC



With r changing with theta you're essentially changing the length of the string dependant on the angle.



Think again. r is not simply the string length. hug





Coleman, you have about 30 hours to go to that exhibition at victoria Miro gallary.

tomorrrow is last day.



http://www.victoria-miro.com/usr/images/artworks_detail/cs21_binarystar2_2006.jpg
br>


Binary Star, 2006, is the latest in Shawcross's series of kinetic light works

Its a mechanical poi spinner init biggrin

EDITED_BY: Glss (1163762628)


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NYC


NYC

NYC
Location: NYC, NY, USA

Total posts: 9232
Posted: Written by: Glss



Think again. r is not simply the string length. hug




Oh don't pull your Yodadrew and be all vague until I get frustrated and give up on what you're actually trying to say. tongue

I'll try to understand once:

Glass: "NYC, r is not the total length of the string but the effective length of the string at any given moment. For example, in a hyperloop, r would be the distance from where the strings cross to the center of mass of the poi."

NYC: "Yeah, I know that, that's what I was calling 'string length'..."

Glass: "But it's not the total string length"

NYC: "I know. Just the length of the string from the center of it's curve to the poi. Got it. Like if you're swinging poi and the string goes from the poi, through your hands and down your pants (see my lightbulb poi) you obviously wouldn't count the length of the wire down my pants."

Glass: "Nor would you count the portion of the string from a hyperloop nexus to your hands"

NYC: "Yes, I get it"

Glass: "ShutupIhateyoudie"

NYC: "MCP, give Glass back the keyboard."

MCP: "OK. But I stillhateyoudie."


Well, shall we go?
Yes, let's go.
[They do not move.]

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay

Total posts: 7330
Posted:you're listening man, but you're not *hearing* us, you know?
think pre-string...

clue#onefornyc:
shoulders-elbows-wrists

youalreadygotclue#two:
tangle

clue#three:
isolation



Non-Https Image Link



cole. x


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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mcp
PLATINUM Member since May 2003

mcp

Flying Water Muppet
Location: Edin-borrow.

Total posts: 5276
Posted:Wow, cool, i'm in this thread already!

I like how the diagrams have stick bits in them now... shame my sticks can't change lengths wink

MEG: "I hate you NYC!"

NYV: "I know!"

<meg skips off into the hills with heidi>


"the now legendary" - Kaskade
"the still legendary" - Kaskade

I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.

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Glåss
DIAMOND Member since Nov 2001

Glåss

The Ministry of Manipulation
Location: Bristol

Total posts: 2523
Posted:Meg, who's heidi, is she your new bird?

r= f( upper arm length and upper arm angle,
forearm length and forearm angle,
hand length and hand angle,
string length and instantaneous string angle)

Include a sprinkling of sin or cos to construct complete the function
and if you wish boundaries on the limits of angles constrained by realistic biological constraints

If you want to complicate things you should also include a term for the displacement of the shoulder from the origin. but for the sake of simplicity I'm taking a shoulderocentric view of the poi spinning universe.)
and the earth is flat

Bloody high school science teachers
Glass apparently said:"ShutupIhateyoudie" tongue


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NYC


NYC

NYC
Location: NYC, NY, USA

Total posts: 9232
Posted:See, this is what I'm talking about.

Do you really think that I don't understand that the center of rotation for "giant" is the shoulder and a traditional isolation is the center of the string?

If the Coleman's mom is holding poi and I grab her by the ankle and swing her around in big circles than r=(distance from center of rotation of shoulder to hand) + (distance of coleman's mom's ankle to poi string) + (distance of string from finger to poihead)

Now yell at me that the string (and Cole's mom) has mass and the center of mass wouldn't be at the poi head would it?

Plus, you knuckeheads aren't taking gravity into account so it wouldn't be circular would it?

tongue


Well, shall we go?
Yes, let's go.
[They do not move.]

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mcp
PLATINUM Member since May 2003

mcp

Flying Water Muppet
Location: Edin-borrow.

Total posts: 5276
Posted:Equations like these I particularly love, cos I can solve them by spinning.

glass: eh? I mean this heidi: http://images.amazon.com/images/P/0517189674.01.LZZZZZZZ.jpg


"the now legendary" - Kaskade
"the still legendary" - Kaskade

I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.

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Glåss
DIAMOND Member since Nov 2001

Glåss

The Ministry of Manipulation
Location: Bristol

Total posts: 2523
Posted:Colemans mom is well 'ard,

I know smile from experience.



You wouldn't get very far if you swung her round by her feet.

I think thats an impossible example, you should try another one, one thats more realistic.



What you meant to say was:

"With r changing with theta you're essentially changing" THE DISTANCE OF THE POI HEAD FROM THE SHOULDER "Dependant on the angle."



or in other words we're not spinning a basic circular path (where r= constant)



In first 2 equations at top, Alpha is the length of arm plus length of poi,as it happens in those 2 equations, the poi length can be taken as alpha/2.



NYC, you in detention for trying to poi with one of the other bored members mothers, write out 100 times:

r is not a constant, and it is not the poi length.



now I've stopped being rude:

http://functions.wolfram.com/ElementaryFunctions/Sin/visualizations/2.html
br>
http://functions.wolfram.com/ElementaryFunctions/Cos/visualizations/2.html
br>
original post is easier to understand here:

http://mathworld.wolfram.com/Rose.html
br>


Off topic: eeeew MCP You're more of a pervert than that Jareth the goblin king out of Labyrinth

he liked little girls too ubbrollsmile eek ubblol

EDITED_BY: Glss (1163778506)


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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay

Total posts: 7330
Posted: Written by: NYC



See, this is what I'm talking about.



Do you really think that I don't understand that the center of rotation for "giant" is the shoulder and a traditional isolation is the center of the string?





erm, what was it you said earlier...?



 Written by: NYC



With r changing with theta you're essentially changing the length of the string dependant on the angle. Would be tricky but interesting to do in reality.





so yes, i think you didn't grasp the concept that to 'change r with theta' all you have to do is bend your arm rather than 'change the length of the string'.



and i also think that now you are trying to save yourself from looking like a absolute complete and total cretin by backtracking faster than ted haggard and attempting to divert attention away from your idiocy by slagging my mum off (who you know can kick your sorry arse without even breaking a sweat) and pretending to get all indignant on us.





so, just to make it clear (cos i reckon you're still just feigning understanding so as not to attract yet more ridicule from those who were once your peers but now are as gods you look up to):



you suck like a vacuum pump.





and we don't need to 'take gravity into account', bitch - this is poi pattern theory, not an exercise in modelling.



tongue





cole. x


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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Durbs
BRONZE Member since Sep 2001

Durbs

Classically British
Location: Epsom, Surrey, England

Total posts: 5688
Posted:(psst...you forgot to call him gay)

Burner of Toast
Spinner of poi
Slacker of enormous magnitude

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mcp
PLATINUM Member since May 2003

mcp

Flying Water Muppet
Location: Edin-borrow.

Total posts: 5276
Posted: Written by: Glss


Off topic: eeeew MCP You're more of a pervert than that Jareth the goblin king out of Labyrinth
he liked little girls too ubbrollsmile eek ubblol



Dude! When do you think that book was written? She's all grown up now!

Hmm, I think many things make more sense than this post.


"the now legendary" - Kaskade
"the still legendary" - Kaskade

I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.

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NYC


NYC

NYC
Location: NYC, NY, USA

Total posts: 9232
Posted: Written by: coleman


 Written by: NYC


With r changing with theta you're essentially changing the length of the string dependant on the angle. Would be tricky but interesting to do in reality.



so yes, i think you didn't grasp the concept that to 'change r with theta' all you have to do is bend your arm rather than 'change the length of the string'.

and i also think that now you are trying to save yourself from looking like a absolute complete and total cretin by backtracking faster than ted haggard and attempting to divert attention away from your idiocy by slagging my mum off (who you know can kick your sorry arse without even breaking a sweat) and pretending to get all indignant on us.




1) You're totally right that it would be easy to change R by incorporating body parts into the equation. That's why you get such cool trails when you switch from isolated to giant and back. There are many ways of changing r other than by changing the string length.

I was initially defining r as the string length. Glass and Cole were correct in suggesting that that definition was limited. I will now redefine my definition to that. That's not backpetalling. It's me not understanding something.

2) My indignancy comes from my complete disagreement with some folks' educational philosophy. This is an old issue.

Everyone has the right not to teach someone something. If I don't understand something, I have complete respect for someone saying "I don't care" or "I don't want to teach you" or "IHateYouDie." What I have always had issue with is the philosophy of purposely frustrating and embarasing someone under the GUISE of teaching them.

This obviously goes way outside the realm of poi and way outside the realm of this conversation.

This also becomes difficult for you to understand Cole since you are the most generous and patient poi teacher that I've ever had. [A telling statistic considering it's only been an hour in Bam's backyard and three workshops.]

All anybody needed to say was "Hey NYC, you're forgetting the distance from the center of the circle to the outside which could be from the elbow, wrist, shoulder, or any other place." Which is a concept you all KNOW I already understand.

Rather than this "Think again" "You're wrong but I'm not going to tell you why" "Go off and think about it" "Haa haa, let's embarass him because he's defining r incorrectly but nobody tell him the right definition because it's more fun to do it this way."

Obviously I don't really care about being embarrased (or I wouldn't be here on HoP) but any demeaning and counter productive educational philosophy that I take offense to. Again, not solely related to this thread or this topic or poi or HoP or Cole's mom.

tongue


Well, shall we go?
Yes, let's go.
[They do not move.]

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NYC


NYC

NYC
Location: NYC, NY, USA

Total posts: 9232
Posted: Written by: mcp


 Written by: Glss


Off topic: eeeew MCP You're more of a pervert than that Jareth the goblin king out of Labyrinth
he liked little girls too ubbrollsmile eek ubblol



Dude! When do you think that book was written? She's all grown up now!




You're right. And since the book was written in 1880 that means she's well over 120 years old. Which essentially makes you a necrophilliac.

Gross Gross Gross Perv.


Well, shall we go?
Yes, let's go.
[They do not move.]

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay

Total posts: 7330
Posted:as a teacher i reckon you are probably quite good at spotting the 'gaps' in someone's knowledge.
others are not so good at this shrug

having said that, i thought that drew's statement that 'r is not string length' combined with my 'clues' would have been enough to highlight to you your erroneous definition of r without the need for someone to say 'r includes your arm and so can be changed by bending your arm at the elbow or wrist or by adding isolation or tangles into the pattern'.

when you then get all shirty and say stuff like: "Do you really think that I don't understand that the center of rotation for "giant" is the shoulder and a traditional isolation is the center of the string?", it seems that you aren't even bothering to see where the difference in understandiong lies and instead you just want us to know what you're thinking and tell you how its different to what we're thinking... shrug

coupled that with the fact that we know you already know the answer ("a concept you all KNOW I already understand."), it gets tricky to see exactly how simply we need to spell it out for you whilst not being condescending.


cole. x


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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mcp
PLATINUM Member since May 2003

mcp

Flying Water Muppet
Location: Edin-borrow.

Total posts: 5276
Posted: Written by: NYC


 Written by: mcp


 Written by: Glss


Off topic: eeeew MCP You're more of a pervert than that Jareth the goblin king out of Labyrinth
he liked little girls too ubbrollsmile eek ubblol



Dude! When do you think that book was written? She's all grown up now!




You're right. And since the book was written in 1880 that means she's well over 120 years old. Which essentially makes you a necrophilliac.




You say she's dead, I say she's obviously an immortal superior being. Win.


"the now legendary" - Kaskade
"the still legendary" - Kaskade

I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.

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