How many triangles can you form in a hexagon

Thus the correction term for false triangles is. The correction is 0 for odd N. The number of triangles formed by line segments with six endpoints on the polygon is then:.

The table below summaries the results for. These values were checked through use of a computer program performing an exhaustive search. The sequence formed by the total number of triangles was studied by the late Victor Meally in the 's, although it appears he did not find our formula for the N -th term. To summarize the final result, the number of triangles generated by intersecting diagonals of an N -regular polygon is:.

Note that Theorem 1 has a typographical error: in the second line: should be replaced by Triangles with 3 diagonal endpoints. Triangles with 4 diagonal endpoints. Triangles with 5 diagonal endpoints. Triangles with 6 diagonal endpoints. Total Number of Triangles. In a hexagon there are six sides. Polygon and its Classification. Terms Related to Polygons. Interior and Exterior of the Polygon.

Convex and Concave Polygons. Regular and Irregular Polygon. Number of Triangles Contained in a Polygon. Angle Sum Property of a Polygon.

I can see 35 in a pentagon, by organising my triangles by the quantity of shapes each is constructed of:. Total of 35 triangles. Sign up to join this community. The best answers are voted up and rise to the top.

Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How many triangles can we form if we draw all the diagonals of a hexagon? Ask Question. Asked 9 years, 8 months ago. Active 5 years, 11 months ago. Viewed 24k times. Hiro Nakamura Hiro Nakamura 1 1 1 gold badge 1 1 silver badge 1 1 bronze badge. Convex or not?

Regular or not?