Talk:Deltoid curve

Proposed move

I propose moving this to Deltoid curve, and redirecting Tricuspid curve there. Gene Ward Smith 23:11, 14 May 2006 (UTC)

Animation

I removed this graphic when I added the animated deltoid figure. Just in case someone wants to put it back.Doctormatt 03:23, 24 August 2006 (UTC)

Inanimate object

The "animation" of the deltoid curve "shown in red" does not move for me, there is just a red ¿starting? dot. Is it me or The System?

It works fine on my machine and as far as I know it's a standard animated GIF. Perhaps the entire file didn't get loaded for some reason when you tried it.--RDBury (talk) 00:53, 22 November 2009 (UTC)

in other words, essentially the same words

... it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three times its radius. It can also be defined as a similar roulette where the radius of the outer circle is three times that of the rolling circle.

These "two" definitions look practically identical to me. —Tamfang (talk) 22:59, 14 October 2011 (UTC)

I'll have to look at the wording in context but there are two different sizes of circles which, when rolled inside the same circle, generate the same curve. With one exception, all centered trochoidal curves (Limaçon, nephroid, deltoid, etc.) have this double generation property.--RDBury (talk) 18:18, 16 October 2011 (UTC)

The original was changed a while ago by an anon trying to "correct" what was thought to be an error. I changed it back.--RDBury (talk) 18:55, 16 October 2011 (UTC)

Inconsistent Title Naming?

The AstoidAstroid article doesn't have curve within the title but this one does. I think we ought to remove the curve and just call the article Deltoid --Pithon314 (talk) 00:48, 20 December 2019 (UTC); edited 08:01, 14 December 2020 (UTC)

I urge you to look at Deltoid. —Tamfang (talk) 00:34, 21 December 2019 (UTC)

Ambiguous parametric equations

The parametric equations are given as

$x=(b-a)\cos(t)+a\cos \left({\frac {b-a}{a}}\right)$

$y=(b-a)\sin(t)-a\sin \left({\frac {b-a}{a}}\right)$

which are the same ones for a hypocycloid. However, these apply for any hypocycloid. For a deltoid, the following must apply.

${\frac {b-a}{a}}=2$

As written, I believe this is not emphasized enough. Rchensix (talk) 21:20, 28 December 2020 (UTC)

Is this the right equation?

The sections Equations contains this passsage:

$z=2ae^{it}+ae^{-2it}$

The variable t can be eliminated from these equations to give the Cartesian equation

${\color {Red}(x^{2}+y^{2})^{2}+18a^{2}(x^{2}+y^{2})-27a^{4}=8a(x^{3}-3xy^{2})}$

The top equation is correct for the deltoid.

But in the lower equation (in red), in terms of x and y, I have plotted this carefully for a wide range of values for the constant a, but none of the resulting curves look anything like the deltoid. (Although they do have threefold symmetry.)

I hope someone familiar with the deltoid can supply the correct formula (and/or the range of a).— Preceding unsigned comment added by 2601:204:F181:9410:10AD:61E0:72E5:372D (talk) 19:09, 8 December 2024 (UTC)