# Divide a triangle into fourths with greatest angle?

**URL:** <https://community.wolfram.com/t/divide-a-triangle-into-fourths-with-greatest-angle/10001>\
**Category:** Questions\
**Tags:** fun-and-play, geometry, graphics-and-visualization\
**Created:** [February 8, 2017, 11:16pm UTC](https://community.wolfram.com/t/divide-a-triangle-into-fourths-with-greatest-angle/10001 "2017-02-08T23:16:54Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![22padrinos](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/22padrinos/32/29645_2.png) [@22padrinos](https://community.wolfram.com/u/22padrinos)\
**Post date:** [February 8, 2017, 11:16pm UTC](https://community.wolfram.com/t/divide-a-triangle-into-fourths-with-greatest-angle/10001/1 "2017-02-08T23:16:54Z")

</div>

Hello everyone, I am doing the following experiment with triangles, the idea is the following, we take a triangle in space, for example the triangle with points A (0,0,0), B (0,60,0), C (80,0,0) then we look for the largest angle of said triangle, after analyze the angles of the triangle we see that the larger angle is what is at the point {0,0,0,}, subsequently we construct a straight line to the midpoint of the opposite side to the point {0,0,0}, finally we estimate the midpoints of the sides adjacent to the point {0,0,0} and the join by a straight line to the midpoint of the opposite side that we calculated above.

The way I have done it is the following, but the problem is that I do not understand why I have empty spaces between divided triangles as seen in the following image

 ![emptyspace.jpg](https://global.discourse-cdn.com/wolfram/original/3X/a/3/a3da98c792789dd0d7b344e8da5d4c8f11cffdc4.jpeg)

 ![holes.jpg](https://global.discourse-cdn.com/wolfram/original/2X/1/1dc53ca199e53b5c326ceffe6cea0fe03887626f.jpeg)

I hope someone can help me find the fault,I do not think there should be such holes. Please see the notebook add.

Greetings to all.

---

<div class="post-metadata">

**Author:** ![sukrause](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sukrause/32/41348_2.png) [@sukrause](https://community.wolfram.com/u/sukrause)\
**Post date:** [July 20, 2017, 2:26pm UTC](https://community.wolfram.com/t/divide-a-triangle-into-fourths-with-greatest-angle/10001/2 "2017-07-20T14:26:43Z")

</div>

Obviously the new triangles are not complanar with the plane of the very first triangle. Therefore you look _through_. If you could convince yourself to ease things as much as possible you would

- first transform your very first triangle into a co-ordinate plane
- second do all calculations along the lines of [Divide a triangle into four small triangles](https://wolfram.discourse.group/t/4090/1) in two dimensions only
- third transform the result back

thus avoiding any problems with complanarity.