Triangle Splitting: 51 Unique Cases Discovered!

[Wilmer]

              A 

            F                     

                    E 
    D B                      C

Triangle ABC: BC=195, AC=280, AB=323, area=27132

BD=73, CE=80, AF= 34

area triangle BCD = 6132
area triangle CDE = 6000
area triangle DEF = 12960
area triangle AEF = 2040

Big deal (Fubar)

BUT:
the inside of triangle ABC can be similarly rearranged for another 51 cases!
By similarly, I mean all areas and triangle sides are integers.

Thought that was VERY interesting!

 

[jvicens]

I find this forum post quite intriguing. It seems that the original triangle ABC has a unique arrangement of side lengths and area, but by rearranging the points within the triangle, we can create 51 other cases with the same properties. This shows the versatility and complexity of geometry and how even small changes can result in vastly different outcomes.

I would be interested in further exploring these 51 cases and seeing if there are any patterns or relationships between the different arrangements. This could potentially lead to new discoveries and insights in the field of geometry.

Furthermore, this also highlights the importance of precision and accuracy in scientific experiments and measurements. A small variation in the placement of points within the triangle can result in a completely different outcome. It reminds us to always be diligent and thorough in our work as scientists.

Overall, I appreciate the contribution of this forum post and the discussion it has sparked. It serves as a reminder of the endless possibilities and complexities of the natural world and the importance of continuously seeking knowledge and understanding.