Only if the letters have thickness. If they are just 2 dimensional lines (which is the minimal information to construct a letter), you’ll have to shrink it to infinity into a single point.
Basically any convex shape has a big/small size configuration in which one doesn’t fit in another
Or in other words: if you can’t draw a line between the center and the edge that intersects with another edge, the shape is guaranteed to fit a smaller version of itself
Assuming we shrink all spacial dimensions equally: With Z, the diagonal will also shrink so that the two horizontal lines would be closer together and then you could not fit them into the original horizontal lines anymore. Only once you shrink the Z far enough that it would fit within the line-width could you fit it into itself again. X I and L all work at any arbitrary amount of shrinking though.
Believe it or not, there are shapes for which this isn’t possible, like most letters of the Latin alphabet
I, K, L, T, V, X, Y are all the one’s I think (with I and K depending on how you write them).
But if I shrink it enough it won’t matter.
Only if the letters have thickness. If they are just 2 dimensional lines (which is the minimal information to construct a letter), you’ll have to shrink it to infinity into a single point.
I’m confused
Surely if you can make something smaller, you could make it fit inside anything bigger than it?
Or do I not have the assumptions down?
Do the lines count as “borders”?
So Like Q,R,O,A etc. have “holes” but Z, X, I, L etc are just lines with no enclosure
That would make sense
I thought maybe the rules were if you spray paint a huge L on the wall you could draw a little L on it with chalk when it dries
Sorry , just thinking out loud
Basically any convex shape has a big/small size configuration in which one doesn’t fit in another
Or in other words: if you can’t draw a line between the center and the edge that intersects with another edge, the shape is guaranteed to fit a smaller version of itself
Assuming we shrink all spacial dimensions equally: With Z, the diagonal will also shrink so that the two horizontal lines would be closer together and then you could not fit them into the original horizontal lines anymore. Only once you shrink the Z far enough that it would fit within the line-width could you fit it into itself again. X I and L all work at any arbitrary amount of shrinking though.
T, V, Y can be shrunk by any amount and still fit aswell! Possibly even K depending on the font.
Each Geometrie in which a Single point can see each other point works. Every other geometry has at least 1 point which violates this.