Magic Hexagon

x

2.1

Let

G

be the centroid of the triangle

ABC

. Define

A

1

and

A

2

by

A

1

=xG+(1-x)A

,

A

2

=-xG+(1+x)A

and similarly define the points

B

1

,

B

2

,

C

1

,

C

2

.

The apexes of the equilateral triangles on the outside or inside of the hexagon

A

1

C

2

B

1

A

2

C

1

B

2

form a regular hexagon.

External Links

The Excentral Triangle and a Related Hexagon

A Hexagon with Opposite Sides Parallel

Permanent Citation

Minh Trinh Xuan

"Magic Hexagon"
http://demonstrations.wolfram.com/MagicHexagon/
Wolfram Demonstrations Project
Published: May 13, 2022