17 November 25

August Ferdinand Möbius was born on 17 November 1790. He was a mathematician whose fame circles around the strange properties of the "Möbius loop," portrayed by my tie and by the paper band I'm holding. It's peculiar because the loop has exactly one side. What look like two sides of paper actually form a single surface; if you draw a line around the loop, your pencil will travel twice the "length" of the loop and you will see that there is no "inside" or "outside." If you work to cut a Mobius loop in half (lengthwise), you get another single loop! The original loop has a single twist, and the new loop (which has two surfaces) has two twists.

The curious features of Möbius surfaces have applications in mechanical engineering, manufacturing, chemistry, entertainment and art. All of my students in Beginning Philosophy and Beginning Ethics had fun (?) making Möbius loops and learning about their properties.

17 November 24

For my annual celebration of the birthday (on 17 November) of August Ferdinand Möbius (1790-1868), I'm wearing my self-crafted ribbon Möbius loop. It's a circle of ribbon including a single twist. This object has a single side and a single edge, which you can prove by working to paint the loop or to trace along the edge; as you progress in your work, continuing down the path, you eventually reach the point where you started, having traveled twice the circumference of the loop. Put somewhat differently, what seem to be two sides of the ribbon are just one. Mr. Möbius explored the topology of this kind of object and other continuous surfaces.

17 November 23

August Ferdinand Möbius was born on 17 November 1790. He is most famous for investigating the amazing mathematical and topological properties of what we call Möbius loops. The simplest example is a circular ribbon formed with a single twist. This object has a single side and a single edge, which you can prove by working to paint the loop or to trace along the edge; as you progress in your work, continuing down the path, you eventually reach the point where you started, having traveled twice the circumference of the loop. If you try to cut this loop in half (lengthwise), you get another single loop, twice as big as the original -- but the double-sized loop now has two twists, and has two sides and two edges. That may sound like magic or "child's play" but the fascinating properties have applications in mechanical engineering, biology, chemistry and art. Many works by M. C. Escher involve Möbius loops; you can watch a video recreating Escher's red fire ants crawling on a loop! Dr. Möbius made many other contributions to topology and theoretical mathematics. My tie is a Möbius ribbon. Today in my Beginning Ethics class I'm helping my students appreciate the wonders of Möbius loops using long paper strips, tape, pencils and scissors!

18 November 22

August Ferdinand Möbius was born on 17 November 1790. He is most famous for investigating the amazing mathematical and topological properties of what we call Möbius loops. The simplest example is a circular ribbon formed with a single twist. This object has a single side and a single edge, which you can prove by working to paint the loop or to trace along the edge; as you progress in your work, continuing down the path, you eventually reach the point where you started, having traveled twice the circumference of the loop. If you try to cut this loop in half (lengthwise), you get another single loop, twice as big as the original -- but the double-sized loop now has two twists, and has two sides and two edges. That may sound like magic or "child's play" but the fascinating properties have applications in mechanical engineering, biology, chemistry and art. Dr. Möbius made many other contributions to topology and theoretical mathematics. My tie is a Möbius ribbon. Today in my Beginning Ethics class I'm helping my students appreciate the wonders of Möbius loops using long paper strips, tape, pencils and scissors!

24 June 21

 Happy Birthday to my first nephew, C. Nolan Huizenga! He's been the associate pastor at Second Presbyterian Church in Nashville, TN, but he and his wife Aimee Moiso are starting a new volume in their lives as they move to Louisville, KY where Aimee will be Associate Director at the Louisville Institute. Nolan asked me to wear this Möbius-themed tie loop "because I love the conjunction (continuity?) of science and art." A Möbius loop is a very simple shape that is a continuous surface with just one side. You can make one yourself from a long strip of paper, attaching the ends with a single twist. When you trace the surface with a pen or your finger, you discover that it has exactly one side (and one edge)!

19 November 18

My tie today is very one-sided. It's a Möbius loop, to honor the birthday (on Saturday, 17 November) of August Ferdinand Möbius (1790-1868). He was a German mathematician who first explored the topology of the loop/strip that bears his name. It's a one-sided loop, meaning that you can travel the entire surface of the loop without ever crossing an edge or "getting to the other side." You can play with one on your computer monitor from this Wikipedia page, but it's even better to make your own from a wide strip of paper that is at least 11 inches long. Tape the ends together to make a loop, but include a single twist in the loop. Drawing a line down the center of the loop (like the center line on a road) will prove that the loop has only one side -- you reach your starting point again without ever turning the paper over. If you cut down that center line, to "cut the loop in half lengthwise," you get a surprise. Besides their interesting topological properties, Möbius loops have become important elements in art, jewelry, molecular synthesis, and mechanical engines and conveyor belts (where a drive belt can have a longer useful life because the friction-wearing surface is twice as long as a conventional flat belt). I Möbius-looped my tie by inserting the tail into the main part, with a single twist.

16-17 November 17

November 17 marks the birthday of August Ferdinand Möbius, 1790-1868. He is most famous for his mathematical description of the Möbius strip (or loop), which is a looped surface that has only one side. I hope you have had a chance to play with Möbius loops! My tie is made from wide ribbon, and it has only one side. I mean that if you were painting my tie, you could brush smoothly all around the loop until you reached your starting point -- and you would have painted the entire loop -- it has no "inside" versus "outside." Here's your topological/philosophical puzzle for today: In what sense does my tie tack go "through" the loop? We can't say it pokes through "one side" and comes out of the "other side," because the loop has only one side . . . even when I cross the loop over itself . . .

17 November 15

Today is the right day to have a one-track mind! August Ferdinand Möbius was born on this date in 1790. He is famous for studying the properties of the "Möbius strip," the amazing three-dimensional surface that has only one side. Photobucket has some wonderful images of Möbius strip art. Although the paisleys on my tie are not Möbius figures, they are sufficiently loopy to be appropriate for this anniversary.

17 November 14

Today I'm celebrating the birthday (in 1790) of August Ferdinand Möbius, the German mathematician who first investigated the wonderful properties of the single-sided Möbius strip. You can make your own by taking a long narrow strip of paper, like a very long cash register tape or a strip cut from a newspaper double page, and forming a loop with a SINGLE TWIST in it, and then taping it so you can play. (It will seem that you attaching the "front side" of the paper to the "back side" of the other end.) If you now take a pencil and draw a line down the strip -- like driving down the middle of the road -- you can go completely around the loop twice without ever turning the paper over, and you wind up where you started. Your loop has a single side (surface). If you take scissors and cut on the line you just drew, to cut the loop in half "lengthwise," you get a very surprising result.

17 November 13

A little "twisted" humor today, to honor the birthday of August Ferdinand Möbius (1790-1868). He is most famous for exploring the geometric properties of the "Möbius strip," a two-dimensional surface that has only one side. My tie is looped in Möbius fashion (haha), and at Beth's suggestion I have attached a paper Möbius loop!

17 November 11

Happy Birthday, Mr. Möbius! August Ferdinand Möbius (November 17, 1790 - September 26, 1868) was a German mathematician who discovered the unusual properties of the one-sided "Möbius strip" in 1858. You can make one for yourself by looping a long strip of paper, twisting the paper once before fastening it (e.g., with tape) to complete the loop. The surface of this object now has only one side, as you can prove by drawing a continuous pencil line around the loop. The technical definition is "a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space" (Wikipedia, article on Möbius). Möbius-loop patterns are famous in art, particularly in many designs by M. C. Escher, and they are also of increasing interest in chemistry. My tie recreates a one-sided loop to celebrate Möbius' birthday, with animals parading in all possible directions.

17 November 08

August Ferdinand Möbius (November 17, 1790 - September 26, 1868) was a German mathematician who discovered the unusual properties of the "Möbius strip" in 1858. You make one by looping a long strip of paper, twisting the paper once before fastening it (e.g., with tape) to complete the loop. The surface of this object now has only one "side," as you can prove by drawing a continuous pencil line along the path. The technical definition is "a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space" (Wikipedia, article on Möbius). Many of M. C. Escher's drawings are based on Möbius patterns. My tie represents a crude attempt to wear a one-sided loop to celebrate Möbius' birthday.