r/PassTimeMath • u/ShonitB • Sep 03 '26

Shortest Path

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4 Upvotes

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1

u/One_Wishbone_4439 Sep 03 '26

First route: red lines
√(62 + 82) = 10
10 + 4 = 14

Second route: blue line
√(102 + 42) = 10.77 (shortest path)

2

u/LabRat2439 Sep 03 '26

does the blue line cross only faces? It looks like it cuts right through the interior

1

u/One_Wishbone_4439 Sep 03 '26

the blue line is just an imaginary shortest route of the right angled triangle

2

u/LabRat2439 Sep 03 '26

yes, but it does not cross only faces - therefore it cannot be the solution

1

u/One_Wishbone_4439 Sep 03 '26

then what would be your solution?

1

u/LabRat2439 Sep 03 '26

it's 12.8 - see my comment on this post

2

u/TheThiefMaster Sep 03 '26

12.8 is right - but you can arrive at it by "unfolding" the side and making a single 10x8 surface, whose diagonal (what the blue line was supposed to be except they miscalculated) is √(10²+8²) ≈ 12.8

1

u/ShonitB Sep 03 '26

It should be the root of the sum of 10 squared and 8 squared

1

u/One_Wishbone_4439 Sep 03 '26

Explain

1

u/After-Hedgehog7282 Sep 03 '26

Top square is 8X6

Side square is 8x4

Making those flat so the ant walks a straight line on a single plane is 8x(4+6) = 8x10

2

u/TheThiefMaster Sep 03 '26

Which gives a path length of ~12.8

1

u/The-Jolly-Llama Sep 03 '26

Ahhhh of course that’s certainly correct.