|
Search: id:A060782
|
|
|
| A060782 |
|
Degree of the curve C(n) relative to a triangle ABC with side lengths a, b and c, given by (x^n- b^n)(y^n-c^n)(z^n-a^n)=(x^n-c^n)(y^n-a^n)(z^n-b^n) where x, y and z denote the distances from the variable point to vertices A, B and C respectively. |
|
+0
1
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
a(n) is also the degree of C(-n).
|
|
LINKS
|
A. P. Hatzipolakis, F. van Lamoen, B. Wolk and Paul Yiu, Concurrency of four Euler lines, Forum Geometricorum 1 (2001) 59 - 68.
|
|
FORMULA
|
It is known that a(n) = 2n-1 for n even; a(1) = 14; a(3) = 46; and it is conjectured that a(n) = 16n-2 for n odd.
|
|
EXAMPLE
|
C(2) is a cubic curve, the well-known Neuberg cubic of a triangle, so a(2)=3.
|
|
CROSSREFS
|
Sequence in context: A088576 A040190 A163647 this_sequence A040187 A164811 A018813
Adjacent sequences: A060779 A060780 A060781 this_sequence A060783 A060784 A060785
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001
|
|
EXTENSIONS
|
Better description from Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 10 2001
|
|
|
Search completed in 0.002 seconds
|
