Question

Intersecting planes question:
1 plane creates 2 areas
2 intersecting places create 4 areas

Find the equation that would give you the number of areas created when you have n planes.

>given that:
- no 3 planes intersect in a line
- no 4 planes intersect in a point
- no parallel planes

Answer 1

The question that came before this (to give you more context).

In terms of intersecting lines on a 2 dimensional plane
1 line = 2 areas
2 lines = 4 areas
3 lines = 7 areas

The given equation is n(n+1)/2 + 1

Answer 2

Here is what the 3 intersecting lines looked like

Answer 3

This is how 2 intersecting planes have 4 areas

Answer 4

@Ultrilliam this fits your category right o.o more like @Hero

Answer 5

My brother said if it was algebra he would have helped you v.v

Answer 6

I would've helped myself if it was algebra x'D

Answer 7

Lmbo sorries though v.v I would help but only know basic math XD

Answer 8

I determined that 3 intersecting planes should result in 8 areas

Answer 9

@Vocaloid whenever she gets on x'D this isnt math ._. this is torture

Answer 10

Figured out this much

Answer 11

The thing that got cut off:
\[\frac{ n(n+1) }{ 2 } + 1\]

Answer 12

@sillybilly123 some assistance please?

Answer 13

TU Voc for the flattering invitation.

i cannot imagine this pattern beyond the \(\mathcal {R^2}\) bit. so i would follow it in that vein; and had i the time, i would explore the patterns

have a strong feeling that the conclusion is trivial. not least, because it reminds me of this:

https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg

but that a topologist would be horrified by my lack of know-how.

Answer 14

thinking about it, it is a linear algebra question!! to which i do not know the answer.

Answer 15

I went to my professor's office hour

For each plane added, the new plane intersects n(n+1)/2 + 1 many regions
so that many regions are added when a new plane is put in.
n(n+1)/2 + 1 = (n choose 2) + (n choose 1) + (n choose 0)

Answer 16

Then we can represent what I just said as:

Answer 17

From the given pattern, I want to say that:

Answer 18

(and it does work, proved with inductive reasoning process)

Answer 19

oh and the whole "choose" thing...