For questions regarding the definition, properties and applications of Soddy circles, the kissing circles in Descartes' theorem.
Questions tagged [soddy-circles]
17 questions
14
votes
2 answers
What is the name of the circle that is tangent to three mutually-tangent circles centered at the vertices of a triangle?
I want some information about the little 'tangent circle', but I don't have its name to search for it in the internet. What is it called?
JSCB
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12
votes
2 answers
How the recursive structure of Apollonian gaskets can be described in order to be able to reproduce them?
The classical Descartes-Soddy relationship between the signed curvatures $b_k$ ("b" for "bend") of 4 mutually tangent circles (Apollonian configuration):
$$\sum_{k=1}^4 b_k^2=\tfrac12 \left(\sum_{k=1}^4 b_k\right)^2\tag{1}$$
allows to obtain the…
Jean Marie
- 88,997
5
votes
2 answers
To show the center of homothety of the biggest and smallest circle lies in the common tangent over T
$c_1$ centered at $A$ passing through $B$.
$BB′$ is a diameter of $c_1$.
$T$ a random point in segment $BB′$.
$c_2$ centered at $B′$ passing through $T$.
$c_3$ centered at $B$ passing through $T$.
$c_4$ tangent externally to $c_2$ and $c_3$ and…
hellofriends
- 2,048
2
votes
1 answer
Needed explanation on why this magic circle works
Given two distinct points $A$, $B$ and a random point $T$ in between them:
$c_0$ is the semicircle of diameter $AB$, center $C$.
$c_A = \odot(A,AT)$
$c_B = \odot (B,BT)$
$I_A = c_A \cap c_0$ and $I_B = c_B \cap c_0$
$O = I_AI_B \cap AB$
$H_A$…
hellofriends
- 2,048
2
votes
1 answer
Decreasing rings of tangent circles. Solved geometrically/graphically but would like to solve with equation.
Inspired by a geometry workshop analyzing the dome of the Lotfollah mosque in Ifsahan, I started constructing a digital version of the pattern. When following the ruler and compass construction technique in Illustrator, I was encountering some…
Tighe
- 23
2
votes
0 answers
Another approach to Soddy circles formula
I am trying to prove a version of Descartes' theorem in an elementary way.
Given three mutually tangent circles (no one is inside the others) with centres $A,B,C$ and radii $a, b, c$ respectively, I would like to compute the radius of the inner…
mapping
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Need help with a problem regarding Descartes' theorem
I'm working on a general Apollonian gasket (i.e., with no particular symmetry). One example might be to populate a Steiner chain with Apollonian circles. I programmed a recursive Descartes' theorem using the equations given in Wikipedia (Descartes'…
Cye Waldman
- 8,196
2
votes
1 answer
Center of Soddy Circle
Given two points inside the unit circle, $(x_1, y_1)$ and $(x_2, y_2)$, let $C_1$ and $C_2$ be the circles with centers at those points, respectively, which are internally tangent to the unit circle. If $C_1$ and $C_2$ are externally tangent to each…
user63205
1
vote
0 answers
Soddy Line in Slope Intercept Form
Given three coordinates of a triangle, is there a simple technique for representing that triangle's Soddy Line in slope intercept form?
Edit: One of the points on the line (incenter), is super obvious. I guess if any of the other points on the…
alfreema
- 115
1
vote
1 answer
Proving that a circle will contain n lattice points?
A lattice point is a point $(x, y)$ in the plane, both of whose coordinates are integers.It is easy to see that every lattice point can be surrounded by a small circle which excludes all other lattice points from its interior. It is not much harder…
0
votes
0 answers
Find the centre of the circle
So there is a square of 50cm length. There are 3 circle's whose centre's are any 3 vertices of the square.The radius(r1,r2,r3) of these circles can be assumed i.e it is known.
Now a 4th circle exists which lies on the 4th vertices and is touching…
0
votes
0 answers
Drawing the Apollonian gasket
Note: I've already asked a question in a similar spirit to this, but I don't feel like I got my point across so here I am.
I am working on a program that draws the Apollonian gasket fractal. I need help with the complex Descartes theorem. It seems…
zenzicubic
- 453
0
votes
1 answer
Finding radii of three tangent circles given their centers
I'm interested in making a program that draws the [Apollonian gasket][1] fractal. For this, I need a way to find the radii of three mutually tangent Soddy circles given their centers, for example given circles $C_i$ with center $(x_i, y_i)$, I want…
zenzicubic
- 453
0
votes
0 answers
Algebraic solutions to the problem of Apollonius for Soddy circles
I'm interested in making a program that draws the Apollonian gasket fractal. To do this, I need a method to find the center of a circle internally or externally tangent to three Soddy circles. Finding the radius is easy enough to do using…
zenzicubic
- 453
0
votes
1 answer
A question about the Soddy incircle
Let $a$, $b$, and $c$ be the centers of three circles that are mutually tangent, and let $B_r(s)$ be the Soddy incircle, tangent to all three. My question is whether one can disprove the statement: there is a point $x\neq s$ and radii $d_a$, $d_b$…
Thomas
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