I Equation for circle points in 3D

AI Thread Summary
The discussion focuses on calculating the coordinates of points on a circle defined by three points (A, B, C) in 3D space. The user aims to derive an algebraic formula for generating 10 points on this circle, starting by inscribing a triangle from the given points and calculating the lengths of its sides. The radius of the circle is determined using a specific formula linked to the geometry of the triangle. The user seeks assistance in finding the coordinates of the circle's center based on the distances between the points. The conversation emphasizes the need for a non-collinear arrangement of the points to ensure they lie on a circle.
Nikkki
Messages
2
Reaction score
0
TL;DR Summary
Calculate the coordinates of consecutive points based on ABC points lying on a circle in 3D space
Hello,

I am trying to solve a problem and I would like to ask for help.

I have 3 points (A, B, C) in 3D space that are assumed to be on a circle.

EXAMPLE 1
1637915795573.png
1637915918290.png
EXAMPLE 2
1637920200382.png
1637916124402.png

My goal is to create an algebraic formula to calculate the coordinates for 10 points on a circle composed of ABC points at any distance from each other.

1637916560383.png
1637916587355.png

MY IDEA

My first idea was to create a triangle inscribed in a circle from the ABC points and then the radius of the circle.
First, I calculate the lengths of the triangle's legs by recalculating the lengths of |AB| |AC| and |CB| vectors.

1637920433604.png

I calculate the radius length using the formula (https://www.physicsforums.com/threads/equation-of-a-circle-through-3-points-in-3d-space.173847/):
1637920084001.png

And at this step, I have now stopped
 
Mathematics news on Phys.org
The center has a distance r to all these points. Can you find its coordinates as function of e.g. a, (b-a) and (c-a), e.g. the position of a and two sides? This is completely analogous to the two-dimensional problem.
 
  • Like
Likes jim mcnamara
mfb said:
The center has a distance r to all these points. Can you find its coordinates as function of e.g. a, (b-a) and (c-a), e.g. the position of a and two sides? This is completely analogous to the two-dimensional problem.
Thank you for your answer.
I am testing the formula for the circle center coordinates in the "Cartesian coordinates from cross- and dot-products" section on the website : https://en.wikipedia.org/wiki/Circu...sian_coordinates_from_cross-_and_dot-products
 
Hint: think bisector - the problem says 'lies on a circle' which has to imply that the points are not collinear.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top