It's interesting. In 1D space, the only objects we can have are dots and lines. Dots are known by a single quantity, a number. And lines are known with two quantities. A line's length is postive and a dot's length is zero. We can think a line of a set of points, infinitely many.

Now if we expand our space to 2D, we'll have another object. Let's call it surface. A surface can be presented with 4 numbers. A dot has zero-length and a line a positive length. But a surface can be made with infinitely many lines of the same or different length. Many lines of the same length can make an object named square. A surface has a properties which line doesn't have(or it's zero for it): Area.

We can further expand our space to 3D where infinitely many surface could form a new object which can exist only in a 3D space and has another properties.

Unfortunately, my mind cannot imagine more than 3D.

#math #geometry #fun #fun_fact #random_thoughts

#FUN_FACT :

When everyone in the fediverse is all tired and asleep, and have brushed their nice little teeth and been tucked into their nice little beds,
all the bots on https://bots-in.space gather together around the campfirewall and start singing their filk of Men In Tights ...