cssa 23 induction q (1 Viewer)

[Masaken]

consider the tile below consisting of three equilateral triangles of side length 1 unit. [i only have the physical copy so i drew it up as best as i could if it makes no sense pls tell me so i can draw it again:]

prove the following result for positive integers n, using mathematical induction.
an equilateral triangle of side length 2^n units may be covered by the tiles above (in any orientation) such that a single equilateral triangle of side length 1 unit is left over at one of the vertices. the tiles may not overlap.

ok so i have the worked solutions for this but when i read it i just don't get it. how would i go about with this question?? (preferably with some explanations as to why you did what you did) like how would i start?? i got up to n=1 but i didn't know how to visualise or even how to consider going about doing the n=k step... pls help, thanks in advance

 

[scaryshark09]

consider the tile below consisting of three equilateral triangles of side length 1 unit. [i only have the physical copy so i drew it up as best as i could if it makes no sense pls tell me so i can draw it again:]
View attachment 39702
prove the following result for positive integers n, using mathematical induction.
an equilateral triangle of side length 2^n units may be covered by the tiles above (in any orientation) such that a single equilateral triangle of side length 1 unit is left over at one of the vertices. the tiles may not overlap.

ok so i have the worked solutions for this but when i read it i just don't get it. how would i go about with this question?? (preferably with some explanations as to why you did what you did) like how would i start?? i got up to n=1 but i didn't know how to visualise or even how to consider going about doing the n=k step... pls help, thanks in advance

Hint: when you get geometric induction - give up, move on to the next question!

 

[tywebb]

i have the worked solutions for this but when i read it i just don't get it.

Which solutions do you have, CSSA's or mine? I put mine here: https://4unitmaths.com/cssa2023e2-tywebb.pdf

so this is how I did it:

 

[Masaken]

Which solutions do you have, CSSA or mine? I put mine here: https://4unitmaths.com/cssa2023e2-tywebb.pdf

so this is how I did it:

View attachment 39703
View attachment 39704
View attachment 39705

i have cssa's. i'm looking through it now but i'll look at it again tomorrow (bit tired, it's not processing in my mind), but yours is slightly different to how cssa explained it. i kind of do get what's going on, though, i'll look at it again and try to do the q on my own tomorrow, thanks for the help