Möbius Strip

Since I got a hang of math and physic, lets talk about one of its wonder. Möbius strip. Objek simple tapi sarat dengan unsur philosophical and mathematical. Let see you take one strip of paper, and twist it at one end and glue em' up just like a picture above. Now here's where it got tricky, ambil pensel, or pen trace a line alone one side of it, continue tracing them. You will find out, that ia mengambil dua kali pusingan sebelum anda dapat menyambungkan satu hujung ke satu hujung yang lain. This single continuous curve demonstrates that the Möbius strip has only one boundary and one surface. Unlike a ring yang ada dua permukaan dan dua sempadan, Möbius strip hanya ada satu muka dan satu sempadan. What a little big wonder isn't it?

Sebenarnya, I came across this concept sewaktu membaca novel Dan Brown 'Angels and Demons', it was just a slight mention, but it really clicked my curiosity button. Discovered by German mathmatician August Ferdinand Mobius it was a work of genius.

THE FUN PART

Sekarang, take a deep breath. Here's where it gets super interesting. Untuk menambahkan keseronokan, saya memerlukan anda mengambil bahagian secara interaktif. Oh, saya bukanlah membuat open invitation to orgy party, tapi saya nak anda membuat tiga Möbius strip. No silly, saya bukan menyuruh anda strip seperti Möbius (whoever he is).

Pertama, trace satu garisan pada Möbius strip anda di tengah-tengah sehingga ia bertemu. Adakah benar Möbius strip hanya ada satu sempadan dan satu permukaan sahaja?

Kedua, guntingkan ia pada garisan tengah tersebut. Apakah yang anda dapat?

Kedua, menggunakan Möbius strip yang baru, sila trace ia pada 1/3 lebar strip itu. Apakah yang anda dapat? Sila guntingkannya pula, apakah yang anda dapat? Amazing isn' it?

Saya tidak akan memberitahu jawapannya, tapi sekiranya anda melakukannya dengan betul, anda akan ternganga sorang-sorang. Seperti mana saya tiba-tiba termencarut di pagi-pagi buta half-screaming "Holy f**k!!!" ketika melakukannya.

Di sinilah di mana first assumption kita tercabar. This is where physic and mathematic wins.

The equation for the numbers of twists after cutting a Möbius strip is 2N+2=M, where N is the number of twists before and M, the number after. Cutting a Möbius strip, giving it extra twists, and reconnecting the ends produces figures called paradromic rings.

Who would've thought, simple strip like this can produce an amazing wonder. Just remember not to scream too loud.

Tell me what you think about it?