假設有一個數，273吧。
同樣理由，因為
100＝（99＋1）
1000＝（999＋1）
10000＝（9999＋1）
如此類推，所有數，只要數字加起來是3的倍數，這個數就會是3的倍數了。
2013年1月5日 星期六
由信用卡尺寸看黃金比例
黃金比例相信大家都聽過，其實是甚麼呢？
當a和b有以下關係的時候，就會構成黃金比例（
）
經運算後，得到一元二次方程 (Quadratic equation)
以公式
計算，
得到黃金比例值為1.618...
再看一看平日我們用的八達通和信用卡甚至各類身份証、會員卡等，都是類似大小的長方形。
它們的尺寸一般長85.60mm；
寬53.98mm；
信用卡的長寬比是 85.60/53.98 = 1.56， 接近於黃金比例，是事有湊巧還是....
）以公式
計算，得到黃金比例值為1.618...
再看一看平日我們用的八達通和信用卡甚至各類身份証、會員卡等，都是類似大小的長方形。
它們的尺寸一般長85.60mm；
寬53.98mm；
信用卡的長寬比是 85.60/53.98 = 1.56， 接近於黃金比例，是事有湊巧還是....
渡河問題三（一家人過橋）
渡河遊戲三
遊戲中有五個人，希望能順利到達對岸。
但是，由於油燈只餘下不多的燃料，必需於30秒內讓所有人成功過橋。橋每次只能負重兩人。
五個人分別需要1，3，6，8，12秒才能過橋，究竟怎樣才可以全部人安全往河的另一邊呢？
提示：（Mouseover 睇）
解：（真的想不到才看～）
渡河遊戲二（食人族和傳教士）
渡河遊戲二，食人族和傳教士
遊戲中只有三個傳教士和三個食人族，六個人想要成功過河。
但是，在任何情況下，若食人族人數比傳教士多，傳教士就會被吃掉。
船每次可以坐兩個人，究竟怎樣才可以全部人安全往河的另一邊呢？
提示：（Mouseover 睇）
解：（真的想不到才看～）
渡河問題（大豺狼小綿羊一箱菜）
自小就喜歡數學，記得曾經玩過一隻渡河遊戲，今天在這兒和大家分享一下。
遊戲中有大豺狼，小綿羊和一箱菜。男人每次只能運其中一樣。
但是，在無人看管的情況下，大豺狼會吃掉小綿羊；小綿羊又會吃掉一箱菜。
究竟怎樣才可以把全部東西運往河的另一邊呢？
提示：（Mouseover 睇）
解：（真的想不到才看～）
How is it possible to measure the temperature with just a few coloured spheres?- Working principal of Galileo themometers
You may have come across acylinder with many colourful spheres just like the one in the photo below. Have you ever wondered what it is? And what does it do?
It is actually called Galileo thermometer. It consists of a sealed glass tube that is filled with water and several floating glass spheres filled with coloured liquid mixture. The liquid mixture can be alcohol, or water with colourings. Attached to each glass sphere is a little metal tag that indicates the temperature.
Coloured fluid: The amount of fluid added allows all the glass spheres have the exact same density.
Tag: The metal tags are calibrated counterweights. The weight of each tag is slightly different from the others.
Coloured fluid: The amount of fluid added allows all the glass spheres have the exact same density.
Tag: The metal tags are calibrated counterweights. The weight of each tag is slightly different from the others.
So, after the calibrated tags are attached to the glass spheres, the glass spheres will have slightly different density, and the density of them is very close to the density of the water.
When the temperature in the room changes, the temperature of the water in the thermometer also changes, so the density of water changes as it may expand or contracts. Therefore, at any density, some bubbles may float while others sink. And the bubble that sinks the most indicates the current temperature.
For example:
Let’s say that there are five spheres in the thermometer.
The blue sphere (64 degrees) is the heaviest (densest) bubble, and each sphere thereafter is slightly lighter, with the dark blue sphere (80 degrees) being the lightest.
Now, let’s say that the temperature in the room is 76 degrees, then the water in the thermometer is also 76 degrees.
The blue sphere (64 degrees), red sphere (68 degrees) and the orange sphere (72 degrees) is calibrated such that they have higher densities than the water at this temperature, so they sink. The dark blue one (80 degrees) have density lower than the surrounding water, so it float at the top of the thermometer. Since the green sphere (76 degrees) is calibrated to represent the same temperature as the water, it sinks slightly so that it is floating just below the dark blue sphere, indicating the room’s temperature.
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