My New 3D Printer

Just got a Prusa I3 MK3 printer. I ordered the MK2 in June 2017, switched my order to the MK3 in October, which added a few months on to my delivery time. Finally arrived, February 2018. I’m super happy with it so far. Leagues beyond my Tronxy, but I’m keeping it and will still use it.

Here’s a time-lapse video of me assembling it:

The Dilettante – More On Infinity Part 2

Part 2 – Use this one weird trick to show that the number of points in a plane is the same as the number of points on a line, and 3D space, and any number of dimensions

You have a point on a plane, and it has an X and Y coordinate, such as:

point_on_a_plane

You can take the X and Y coordinates, and combine them to make a single, unique number by doing the following:

Take the first decimal place of the X coordinate, and follow it with the first decimal place of the Y coordinate, in this case: 0.32, then the second decimal place of the X and Y coordinates: 0.3250, then the third, fourth and so on to as much precision as you care to have: 0.32502689… this, like any number, can be represented by a point on a line. You can do this for every point on the plane and each point will map to a unique point on a line. Similarly, you can take a point on a line and pair up the numbers to make a unique point on a plane. So, now you have a 1:1 function that maps all the points on a plane to points on a line and vice versa.

Now you can add a third dimension.

X:0.07982
Y:0.92580
Z:0.10458

Combine the decimal places in triplets, so in our example the result will be: 0.091720954885208…

You can keep adding dimensions, and no matter how many dimensions you have, you can use this trick to map all the points in 1:1 fashion to a line.

The amazing conclusion is that the number of points on a line of any length is the same as the number of points on a plane, which is the same as the number of points in any dimensional space.

No Way Dude