Welcome to this week’s Math Munch!
Today we’re going to look at a few examples of going “up a dimension”. Our first example is what got me thinking about this theme. It’s a game called roTopo. (If you have trouble getting it to load, try using a different browser.)
Maybe you have played the game B-Cubed. RoTopo is similar—trace through a sequence of squares as they get eliminated one by one. I like B-Cubed because it combines spatial thinking with strategic thinking—planning ahead. Rotopo, with its twists and turns in 3D, stretches a player’s spatial thinking even further. I hope you enjoy giving it a try! Maybe you could design a roTopo level of your own with a drawing or with some blocks.
What else can we find when we look “up a dimension”? Maybe the most famous theorem in all of mathematics is the Pythagorean theorem. There are several ways we might try to take a^2+b^2=c^2 up a dimension. If we start to increase the numbers in the exponents, like a^3+b^3=c^3, we head in the direction of Fermat’s Last Theorem. If we add more terms, like a^2+b^2+c^2=d^2, we can find distances in 3D instead of 2D.
A right tetrahedron—the kind needed for de Gua’s Theorem.
And if those aren’t enough to make you go “wow”, then you need to hear about De Gua’s Theorem. The Pythagorean Theorem relates the sides of a right triangle. De Gua’s Theorem relates the faces of a right tetrahedron. The sum of the squares of the areas of the the three “leg” faces is equal to the square of the area of the “hypotenuse” face. So wild! You can read a proof de Gua’s Theorem here. The theorem is named for the 18th-century French mathematician who presented it to the Paris Academy of Sciences in 1783 (although it was known to others before him). De Gua’s Theorem in turn is a special case of a still more general theorem. Once mathematicians start upping dimensions, the sky is the limit!
Last up: Bibi-binary. No, that’s not the way that Justin Timberlake counts—although that funny thought is why I Googled “bibibinary” in the first place. But when I did, this totally silly number system popped up!
How to count in Bibi-binary.
Well, I guess it’s not the number system that’s silly so much, since it’s actually just hexadecimal. Hexadecimal is like binary, but up a couple of dimensions. The system uses sixteen symbols to represent numbers, just as the decimal system uses ten symbols and binary uses two. What makes Bibi-binary silly, then, is not its logical structure but how it sounds.
There are sixteen syllables in Bibi-binary, which are made from combinations of four consonants and four vowels. Three is “hi” and eight is “ko”. If you want to have three 16’s and eight more—56—that would be “hiko”. As another example, 66319344 is “hidihidihidiho”. Bibi-binary was invented in 1971 by a French singer and actor named Boby Lapointe.
I think it would be fun to learn to count in Bibi-binary. Can you believe that I could find zero (“ho”) videos online of people counting in Bibi-binary? I wonder if any of our readers might enjoy making one…
Hexadecimal is not just fun and games. It’s also used for making codes to stand for colors, especially in making webpages. Most of Math Munch is either 683D29 or 6AB690, would you believe. You can explore using hexadecimal to name colors in this applet.
You can learn lots more about Bibi-binary on the great website dCode, and you’ll also find an applet there that can convert between decimal and Bibi-binary. DCode has lots of tools related to cryptography (get it?) and other math topics, too.
Do you have any favorite examples of math that goes “up a dimension”? We’d love to hear about them in the comments.
Bibi-bi for now! Bon appetit!