Hey, Vsauce. Michael here. Now, one of my favorite treats of the holiday season is Gabriel's cake. It's a super solid based on Gabriel's Horn that you can make right at home, as long as your home is infinitely large. Okay, all right. Now, the first thing you want to do is bake a cake. I prepared this cake earlier. It's a real beautiful cake. It's a little large, but I bet you I could eat that whole thing in a day if I tried. Am I right? Okay, now the second step is cut the cake in half. Notice that while I cut this cake in half you don't add or create any new cake but the surface area of the cake has increased. It used to be completely covered and now we've got two regions on the inside that aren't covered. The next step is to cut this half, one of the halves, in half. Here we go. Again, the volume of cake on the table is the same as it was in the beginning but the surface area is going up. As you may be able to guess, the next step is going to be to cut one of these quarters of the original cake in half. It's getting pretty thin, but all you have to do is keep this up - cutting halves in half and half and half and half forever and once you've done that, well, you're almost there. When you finish cutting, stack the halves on top of one another in order, like this, to create a beautiful tiered dessert. Because you have an infinite number of thinner and thinner slices when you're done stacking them the cake's vertical height will be endless.

Hey, Vsauce. Michael here. Now, one of my favorite treats of the holiday season is Gabriel's cake. It's a super solid based on Gabriel's Horn that you can make right at home, as long as your home is infinitely large. Okay, all right. Now, the first thing you want to do is bake a cake. I prepared this cake earlier. It's a real beautiful cake. It's a little large, but I bet you I could eat that whole thing in a day if I tried. Am I right? Okay, now the second step is cut the cake in half. Notice that while I cut this cake in half you don't add or create any new cake but the surface area of the cake has increased. It used to be completely covered and now we've got two regions on the inside that aren't covered. The next step is to cut this half, one of the halves, in half. Here we go. Again, the volume of cake on the table is the same as it was in the beginning but the surface area is going up. As you may be able to guess, the next step is going to be to cut one of these quarters of the original cake in half. It's getting pretty thin, but all you have to do is keep this up - cutting halves in half and half and half and half forever and once you've done that, well, you're almost there. When you finish cutting, stack the halves on top of one another in order, like this, to create a beautiful tiered dessert. Because you have an infinite number of thinner and thinner slices when you're done stacking them the cake's vertical height will be endless.