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WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
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Mathematics rating:
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 Field:  Geometry

Definition of parameter t[edit]

I believe that the definition of the parameter t in the Equations section may be incorrect. I think t should the (radian) angle from the x-axis to the line from the origin going through the centre of the rolling circle. I could easily derive the given parametric equations for x and y using this definition, whereas I got nowhere using the given definition: "t is the angle at the origin from the horizontal axis to the ray to a point on the cardioid." Robedavi42 (talk) 18:06, 7 August 2016 (UTC)

Move the graph to the top?

- seconded

Huh?? Why move a chunk of page content off to a subpage? Dysprosia 01:27, 19 May 2005 (UTC)

See Wikipedia:WikiProject Mathematics/Proofs#Cardioid. -- Jitse Niesen 11:33, 19 May 2005 (UTC)


I'm no geometer, but it looks like the cross-section of a globe tomato to me.

It's a butt... —Preceding unsigned comment added by (talk) 08:49, 12 January 2008 (UTC)

Plums are almost always an oval shape. Peaches and apples are much closer to the shape than plums. Apples though are usually round and match the shape perfectly, especially so if they are the sweeter ones that supermarkets sell and people like to eat. Apples are the only decent fit when the cardioid is three dimensions because there is no groove in them (peaches and plums have a groove from top to bottom.)

Tomatoes don't tend to have a stalk recessed into the fruit. Cherries do but they aren't always round and people think of them in pairs.Scottonsocks (talk) 03:57, 9 March 2011 (UTC)


I do not understand how the images can be understood - what are x and y? --Abdull 16:11, 23 May 2006 (UTC)

The Equations section describes x and y in terms of theta. --Jevon 20:39, 25 May 2006 (UTC)
The equations express the rectangular coordinates of the curve, x and y, in terms of a parameter theta. That is, for each value of theta, compute x(theta) and y(theta), and plot the point (x,y) measured x units to the right of the y axis, and y units above the x axis (other direction for negatives). The set of all such points makes the curve shown in the image. So, x and y are just numbers to describe the location of a point on a curve. Dicklyon 22:25, 5 June 2006 (UTC)
The other way to understand the images is to ignore x and y, and just look at rho (radius) and theta. At each angle theta measured from the positive x axis, compute the radius rho and put a point that far from the origin. At 180 degrees, the formula 1+cos(theta) gives zero, so you get a point at the origin, which is the cusp. By displacing theta, or using sin instead of cosine, the whole picture just rotates around that cusp. Dicklyon 22:29, 5 June 2006 (UTC)

IMHO it should be merged with/into Heart (Symbol)[edit]

IMHO it should be merged with/into Heart (Symbol) --Wulf 03:17, 5 June 2006 (UTC)

Absolutely not. Read the article. The two shapes are not the same. Dysprosia 03:23, 5 June 2006 (UTC)
That's almost as bad as calling a trapezoid a squashed square. --ssd 07:14, 26 August 2007 (UTC)
Whaddaya mean? A squashed square is a great explanation to start out with. It is something easily recognizable from kindergarten. You must begin somewhere recognizable and advance once the audience comprehends. I love all the images: Coffee cup, Spirograph(TM), Apple with grid, Apple with microphone stem. That moving Spirograph was great, plus being near the top! It instantly lets reader know. A picture's worth 1000 words. They can rest after that. Kristinwt (talk) 18:03, 4 May 2012 (UTC)

If you want to know r=4*sin-1((sin(O/2)(3/2))) graphs a better "love heart" shape [Matthew Schimpf 7:15 11 March 2009] —Preceding unsigned comment added by (talk) 10:17, 11 March 2009 (UTC)

The caustic seen at the bottom of a coffee cup[edit]

It's a nephroid. I have solved this problem. —Preceding unsigned comment added by (talk) 11:49, 29 October 2007 (UTC)

As the article states, it may be a cardioid, and it may be a nephroid. It depends on the angle of the light rays relative to the bottom of the cup. Cheers, Doctormatt 17:58, 29 October 2007 (UTC)

Merge with Cardioid/Proofs[edit]

It should be possible to simplify and summarize the material in Cardioid/Proofs so that it can be merged into the main article. In addition, the article name 'Cardioid/Proofs' does not conform to Wikipedia naming conventions. Therefore I propose that the other article be merged with this article.--RDBury (talk) 04:59, 12 December 2009 (UTC)

Frankly, I'm not convinced that any of the material in Cardioid/Proofs is worth including in the main article. The results proved there seem simple enough that they could easily be stated without proof, and adding any portion of those derivations here would clutter up the article. Jim (talk) 07:31, 13 December 2009 (UTC)
I tend to agree for the most part and I'll go through the proofs article with a critical eye before doing a merge.--RDBury (talk) 07:13, 14 December 2009 (UTC)
I went ahead and did the merge. I took some parts of the page in very summarized and altered form to add to the main article without disturbing the prose style. The old page is still there with the history so it can be restored if someone objects strongly.--RDBury (talk) 08:22, 14 December 2009 (UTC)

Are the parametric equations correct?[edit]

Other sources give them as:

x = a cos t (1 - cos t) y= a sin t (1 - cos t)

These are not equivalent to those shown in the article. —Preceding unsigned comment added by (talk) 08:34, 20 November 2010 (UTC)

Also, the equation for the area enclosed by a cardioid appears to be incorrect. Instead of A = 6*pi*r^2, isn't it A = 3*pi*r^2/2? Or am I off my rocker? — Preceding unsigned comment added by (talk) 11:53, 7 October 2011 (UTC)

Your a corresponds to the radius to the centre of the circle rolling round, i.e. the diameter of the small circle rather than its radius. The equations are the same otherwise except x is offset a bit. Dmcq (talk) 12:45, 7 October 2011 (UTC)

Length of curve[edit]

Given the parametric equations used in the article, I think the arc length should be 16a not 8a. The 8a length relates to the parametric equations: x = a cos t (1 - cos t) y= a sin t (1 - cos t) which describe a smaller cardioid that the parametric equations shown in this article. Also, the formula for area will need to be adjusted. —Preceding unsigned comment added by (talk) 19:33, 20 November 2010 (UTC)

what is t?[edit]

In the equations, for example; x = a(2cos(t)- cos(2t)) Is t the angle? Is it in degrees or radians? — Preceding unsigned comment added by (talk) 14:11, 13 November 2015 (UTC)

Yes, it's the angle. It doesn't matter whether it's in degrees or radians, since you still end up with the same cosine (e.g., cos(90°) is the same thing as cos(pi/2). Loraof (talk) 16:11, 19 November 2015 (UTC)


DOESN"T THE CARDIOID LOOK LIKE A BUTT? (talk) 22:45, 29 June 2016 (UTC)