Beautiful numbers 數字的美麗

Beautiful numbers 數字的美麗

20th December 2018 0 By livinguktaiwan

On the face of it STEM (Science, Technology, Engineering and Mathematics) seems like a difficult and dry subject.  You have to be quite clever or knowledgeable to contribute to it. That’s true to a certain extent, but I believe it’s possible to make a dry subject interesting and inclusive for the masses with beautiful numbers. That’s what I’ve tried to do today. I’m not going to go into theories and equations to explain thing. I want to share some interesting facts with you so you can feel comfortable around STEM.

I’ve always been really rubbish at maths (you can tell I’m a Brit, as Americans would have called it math) and just about scrapped through my maths exam. That’s a bit of an irony for someone who used to work finance. But then my work involves more than just numbers that’s why I never got fired from my job. Anyway, unless you’re bit of a maths nerd like my other half, maths can be quite a bore. That’s until I glanced through some of his books such as these.

I read bits of it, and found parts that are quite interesting for ‘normal’ people like me. Here are some of my favourite discovery.

Solitude Seven

If you take any number from 1 to 10, you’ll find that 7 is very different from the rest. You can multiply 1, 2, 3, 4 or 5 by 2, and the answer is less than or equal to 10. 6, 8, 9 and 10 can be divided by either 2 or 3 and the answer is still less than 10. Have you noticed which number doesn’t appear in the above? That’s right, Solitude Seven. It really doesn’t have any friends. Does that make it Solitude or Special Seven? Maybe that’s why James Bond is called 007, he’s a bit of a loner as well.

The Phoenix Number

Does that sound like a beautiful name? What number would you give it? Well, just so you know, it’s 142857. You’re probably thinking why such a random number?


The Phoenix number is special because when you multiply it up to 6, all the answers are its own repeated anagram. Let me show you what I mean and it will be much easier to understand.

Each of the answer is embedded in the reciprocal of the initial number 142857.  It just moves backwards and forwards along the spectrum.

And finally if you multiply the Phoenix number by 7, do you know what number you get? 999999. Weird how numbers work right?

Well, that’s not the weirdest thing about the Phoenix number and 9. If you split it into three pairs of numbers 14, 28 and 57 and add them up, the total is 99. Then if you split it into 2 pairs of 3 digit numbers, 142 and 857 and add them together,  you get 999.

Finally, if you square 142857 you get 20408122449. Ok, that’s a really long number. Let’s break it down to two sets of 5 and 6 digit numbers so we get 20408 and 122449. Now add them together and see what number we get? It’s not 9 this time. We’re back to 142757 were we started off. Fascinating right?

So what?

That’s the question you’re probably thinking now. What’s the big deal with 7 being different? Who cares what numbers add up to 99 or 999? What use is all this to me?

Sometimes in life, you don’t need an answer to everything. Appreciating how things turn out naturally, and how beautiful numbers are is a learning of its own. Hopefully you find STEM a lot more friendlier now.

Reference : Alex through the looking glass. How life reflects numbers, and numbers reflect life. By Alex Bellos.

一直覺得STEM (Science, Technology, Engineering and Mathematics) 頗沉悶又比較學術性, 縱使讀過三幾年書,但我懂的真不多。 其實想深一層STEM一直在我們日常生活中出現, 只是我們沒有發覺。 今天不用理論,不用方程式,跟大家分享一些冷知識 。希望未來日子STEM能普及化,大家也可以一起參與。

數學從來都不是我的強項, 但家中另一半也算是精通數學。 見他的書櫃上有好幾本跟數學有關的書,無聊翻看一兩本,發現原來也有一些有趣的資料。跟大家分享。


從1至10 ,10個數目字當中,7也算是頗特別。 如果把1,2,3,4或5剩以2,答案是不超過10。6,8,9和10可以除以2或3,答案同樣小於10。有留意那位朋友沒有出現? 就是孤獨7。 它獨行獨斷,跟其他數字完全沒關係。 我覺得有點像特務007在孤軍作戰。


一個很美麗的名字。你覺得會是哪個數目字呢? 答案是142857。看來是一組很隨意的數目字。

鳳凰數字特別之處,如果你把它倍上至六倍,答案是它自己的變化。 看看這個圖會較容易明白。

每一個答案其實是它重覆自己當中的幾個數目字。 只不過是來來回回有不同的起點和不同的終點。讓我們繼續把鳳凰數字乘以7,看看又如何。 今次答案有變化,剛好是999999。 很神奇喔!

其實神奇的事不止這樣。 鳳凰數字6位數,可以把它拆成3對兩位數字,14,28和57。 把3對數字加起來,答案是99。 又或者我們可以把它拆成兩串3位數字,142和857。 它們的總和是999!

最後我們算一算鳳凰數字的平方吧。答案是20408122449。 這有點長,不如把它拆開成兩串數字20408,122449。 你猜總和是什麼? 今次跟9沒關係啦。 答案是142857。 原來兜兜轉轉又回到起點。 這個世界很妙喔!


你可能會問 so what? 7 跟其他數字沒關係又如何? 誰懶得理哪個數字組合總和是99或999? 這所有跟我有何關係?其實,世上不用所有事情都有答案。 懂得欣賞個中奧妙和數字的美麗,也是一門學問。

參考 : Alex through the looking glass. How life reflects numbers, and numbers reflect life. By Alex Bellos.