Conway Triangle Notation

​
2 Δ
S
A
S
B
S
C
S
ω
4
2
3
2
7
S
S cot A
S cot B
S cot C
ω
4
2
3
2
0.519146
John Horton Conway invented notation that enables more compact formulas for trigonometric functions associated with a triangle.
Let the triangle
ABC
have sides
a
,
b
,
c
; internal angles
∠A
,
∠B
,
∠C
; and Brocard angle
ω
.
Define
S=2Δ=2ABC
,
S
ϕ
=Scotϕ
,
S=
S
A
S
B
+
S
B
S
C
+
S
C
S
A
,
S
A
=ScotA=bccosA=
2
b
+
2
c
-
2
a
2
,
S
B
=ScotB=cacosB=
2
c
+
2
a
-
2
b
2
,
S
C
=ScotC=abcosC=
2
a
+
2
b
-
2
c
2
,
S
ω
=Scotω=
2
a
+
2
b
+
2
c
2
=
S
A
+
S
B
+
S
C
.

External Links

First Brocard Point (Wolfram MathWorld)
Conway Triangle Notation (Wolfram MathWorld)
The Brocard Points and Neuberg Circles of a Triangle
The Conway Circle

Permanent Citation

Minh Trinh Xuan
​
​"Conway Triangle Notation"​
​http://demonstrations.wolfram.com/ConwayTriangleNotation/​
​Wolfram Demonstrations Project​
​Published: May 11, 2022