You are the gold dot, standing in the middle of a ballroom tiled with seven-sided rooms, a floor that cannot exist in ordinary space. Every room on this floor is exactly the same size. The ones near the wall only look small because this window has to squeeze an infinite ballroom into one circle. Drag the floor to walk. The wall will never come closer. It is not a wall; it is infinity.
For the curious kid.
Try to tile your bathroom floor with regular seven-sided tiles and you will fail: their corners are too wide, and three of them won't fit around a point: they overlap. But that is only a fact about flat floors. On a floor that is curved the opposite way from a ball (a floor that flares like a lettuce leaf, with more and more room the further out you go), the corners of a heptagon can be exactly narrow enough that three meet perfectly. That floor is what you are looking at. And it has a wild property: each ring of rooms around you holds more rooms than the last, not a few more but multiplying more, forever. Walk ten rooms in any direction and more of the ballroom lies ahead of you than you have ever seen behind.
Deeper.
For two thousand years geometers tried to prove Euclid's parallel postulate from his other axioms: that through a point beside a line there passes exactly one parallel. Around 1830, Bolyai and Lobachevsky independently stopped trying to prove it and instead denied it, and found not contradiction but a complete, consistent geometry where parallels are plentiful and triangles are always thin. "Out of nothing I have created a strange new universe," Bolyai wrote to his father. This page is that universe, seen through Poincaré's window: a conformal map of the whole hyperbolic plane into a disk: angles are shown truly, sizes are sacrificed, and the boundary circle is infinitely far away.
The floor is the {7,3} tiling: regular heptagons, three at each corner, every interior angle exactly 120°, a thing flat geometry forbids (a flat regular heptagon's corners are 128.57…°, and no amount of shrinking changes a flat polygon's angles; in hyperbolic geometry, bigger polygons have narrower corners, so there is exactly one size of heptagon that works, and every tile here is it). Escher saw a figure like this in a paper of Coxeter's and made it famous as the Circle Limit woodcuts. The museum checked its own floor before opening: the heptagon size was solved numerically from the 120° requirement and agrees with the closed form cosh d = cot(π/7)·cot(π/3) to fifteen decimals, every tile is congruent to machine precision, and three tiles meet at every single interior corner. When you drag, the floor is moved by true hyperbolic isometries, the same rigid motions Bolyai's universe allows, and nothing else.
The wall of this ballroom is drawn one centimeter from your nose, and you will never touch it. Infinity fits in a circle, if the circle is willing to lie about sizes.