Talk:Limaçon

Limacon?

My math teacher says the correct pronounciation is with a "k" sound so it would be said lim-uh-kaun.Cameron Nedland 17:07, 30 December 2005 (UTC)

Based on the spelling with a Cedilla, the ç should be pronounced softly (as the article states) --Dinojerm 04:49, 24 April 2006 (UTC)

Yeah, my teacher is a dumb bitch.Cameron Nedland 20:32, 9 June 2006 (UTC)

Yes, every teacher should memorize every obscure consonant, vowel, and diacritical mark so as to avoid ever misleading a student as to so very important an issue as the pronunciation of a rarely used technical term. [Pardon the sarcasm. I will mention that we generally need to keep in mind that despite how uncomfortable we may have been with having made an error induced by unquestioned acceptance of the opinions of someone else, certain inflammatory statements are best left unsaid - ]. 129.176.151.10 (talk) 21:28, 3 September 2018 (UTC)

"Cardiod"?

Cardioid, would be the proper spelling for the bottom-middle visualization. —Preceding unsigned comment added by 70.129.20.141 (talk) 03:43, 3 April 2006 (UTC)

link fix

Could somebody fix the link to cusp in the first paragraph so that it doesn't go to a disambiguation page? I'm not sure which article for cusp it refers to... Ahudson 21:06, 29 March 2007 (UTC)

Done. Cheers, Doctormatt 23:41, 29 March 2007 (UTC)

Circumference

Some qualified person please include the circumference formula for the limacon in this entry.

Thanks —Preceding unsigned comment added by 190.24.55.241 (talk) 19:30, 1 December 2009 (UTC)

a and b

What are b and a in the equation? If we throw out variables, those variables should be defined. Is a the minimum displacement and b the maximum? Or is a the displacement of the rotating circle and b the displacement of the resultant center? You can't just throw out an equation r = b + a cos(theta).. —Preceding unsigned comment added by 69.237.79.147 (talk) 05:31, 26 June 2010 (UTC)

a and b represent constants, not variables. They are used instead of specific constant values to describe the equation generally. Many math textbooks are written this way as well. The form section describes what happens when you use certain values of a and b, and the graphic at the top shows 3 specific examples. Mktyscn (talk) 13:08, 26 June 2010 (UTC)

For abs ( b ) > abs ( a ) you can consider the difference between the two to to be the smallest possible radius r in the polar representation, and their sum the largest; and some other statement of this form might be applicable for the other sense of the inequality. But, as mentioned above, up to translation and rotation, this is a two parameter family of curves, and the parameters do not have to have meanings in and of themselves.129.176.151.11 (talk)

Limacon as Epitrochoid Animation

I tried this, but the Epitrochoid I get when Rolling Circle Radius (Rr) and Fixed Circle Radius (Rf) are equal (Rr = Rf) and some point interior to the rolling circle, could not match a Limacon except for two points on the x axis. Algebraically, the equation for the epitrochoid [x = 2R.cos(t)-d.cos(2t); y = 2R.sin(t)-d.sin(2t) ... R = radii of fixed and rolling circles, d = distance of tracing point from rolling circle center] could not be reconsiled with the limacon equation r = a + b cos(t) Alternatively, is it possible to add a cross reference showing the dimpled Limacon as a special case of Epitrochoid? I can send the animation avi for reference if that could help. Thank you. 202.71.137.98 (talk) 07:50, 2 February 2011 (UTC)Ujjwal Rane

helpful images

I just want to say thank you to whomever made those animations. When I read the introduction, I thought: how can rolling a circle around a circle form any shape other than a circle? The images make it clear. -sche (talk) 20:15, 16 February 2012 (UTC)

See User:Sam Derbyshire/Gallery for other images by the same person.--RDBury (talk) 02:03, 17 February 2012 (UTC)

Roulette parameters and the nature of the limaçon

The article has the limaçon generating diagram at the right.

Construction of the limaçon $r=2+\cos(\pi -\theta )$ with polar coordinates' origin at (x, y)=(1/2, 0)

From this it appears that, with Q = distance of the generating point from the rolling circle's center and with R being the radius of both circles (in particular of the rolling circle), the limaçon:

• is convex if Q/R < 1/2;
• is dimpled if 1/2 < Q/R < 1;
• is a cardioid if Q/R = 1 (with the generating point on the circumference of the rolling circle); and
• has an inner loop if 1 < Q/R < ??

Can this be confirmed with a source and put into the article? Loraof (talk) 19:29, 1 November 2015 (UTC)

There's no explanation that relates the diagram to the constants $a$ and $b$. Whatever it is, it needs to be in the article as well as in the caption to the diagram. 2601:140:8980:4B20:F1FB:4347:328C:ED41 (talk) 16:55, 21 February 2021 (UTC)