Fibonacci Clock: The Geek’s Clock Finally Decoded
Ever wondered how many times a day do you look at the clock? Unfortunately, there’s nothing fancy about it. It’s a plain clock: An analog clock, a digital clock, a clock! Wouldn’t it be exciting to solve a little puzzle each time you set yourself on a quest to decode the time? If this sound exciting to you, then welcome aboard. On this journey, we unravel a clock for the geek in you. Enter Fibonacci clock.
Fibonacci Sequence, FTW.
What’s Fibonacci? Ask me again. Who’s Fibonacci.
Leonardo Fibonacci was an Italian mathematician who was considered to be the most talented western mathematician of the middle ages. Amidst his numerous contributions, he also introduced Europe to the sequence of Fibonacci numbers (the sequence had been noted by Indian mathematicians in the sixth century itself!).
Fibonacci series is a number sequence, in which each number is the sum of it’s preceding two numbers. The series looks like this: 0, 1, 1, 2, 3, 5, 8, etc. Still wondering how did we get this sequence? Here’s how:
0 (Considered as 1st number)
1 (Considered as 2nd number)
0+1=1 (3rd number is sum of previous two)
1+1=2
1+2=3
2+3=5
3+5=8
. . .
The Tale Of Time Telling
Considering the numbers 1, 1, 2, 3 & 5 from the sequence. Quite interestingly, with only these 5 numbers, one can obtain all numbers ranging from 1 to 12:
1=1, 2=2, 3=3
1+1+2=4, 5=5
1+5=6, 2+5=7, 3+5=8, 1+3+5=9
2+3+5=10
1+2+3+5=11
1+1+2+3+5=12
Note: I have resolved the numbers by considering the highest factor first. 2+3=5, 1+1+3=5, 1+1+5=7 are all valid yet ignored, since the factors by their decreasing order of precedence is: 5, 3, 2, 1, 1. So consider 5, 2+3 & 2+5 instead. Bottom line: we try accommodating larger feasible values first.
We now know that hours can be represented by these five numbers. How about minutes? The solution is simple: The same five numbers!
Every number can be multiplied by 5 in order to obtain the nearest 5th minute:
1×5=5
2×5=10
. . .
(2+3+5=10)x5=50
(1+2+3+5=11)x5=55
(1+1+2+3+5=12)x5=60 (=0 minute of the next hour)
Hence, the golden five numbers can help us tell the time. Lets try:
9:42 = (1+3+5):(8×5) = 9:40
13:59 = (1):(11×5) = 1:55
Note: Yes, you can make a Fibonacci clock with minute precision, however we simply rounds off to the nearest lower multiple of 5. Ex: 9:59 = 9:55, 13:01 = 1:00, etc.
The Core Ingredients
The same principle is now employed using 3 colours & 5 boxes: Red, Green & Blue in boxes of side lengths 1, 1, 2, 3 & 5 units of length. Red indicates hour, green indicates minute & blue indicates both hour & minute. The value of hour and minute is deduced from the box size and it’s colour. Let that sink in first. We now take a look at the variety of possible scenarios:
The Rookie
Case 1 (Only Red) : Say red fills the 3×3 box (i.e. box of side length 3 units) then it indicates that the hour value is 3. Since the rest of the boxes are empty, it means the time is 3 o’clock.
Case 2 (Red+Green) : Say red fills the 2×2 box, then the hour value is 2. Say green fills the 3×3 box, then the minute value is 3×5 = 15. Hence, time is 2:15.
Case 3 (Only Blue) : Say blue fills a 1×1 box, that means hour value is 1, and minute value is 1×5=5. Hence, time is 1:05.
The Pro
Case 4 (Red+Blue) : Say red fills the 3×3 box and blue fills the 5×5 box. Then the hour value can be found out by adding the significance of both red and blue (since red purely indicates hour & blue has the component of both hour & minute). This is why the hour value is 3+5, i.e. 8. While calculating minutes, we simply check the side length of the box with blue colour, i.e. 5×5 = 25. Hence, time is 8:25.
Case 5 (Blue+Green) : Say blue fills the 3×3 box and green fills the 1×1 box. Then the hour value can be found out by simply considering the side length of blue box, i.e. 3. For minutes, we must add the significance of both blue and green (since green purely indicates minutes & blue has the component of both hour & minute). This is why minute value is (1+3)x5, i.e. 20. Hence, time is 3:20.
Case 6 (Red+Blue+Green) : Say red fills the 3×3 box, green fills the 5×5 box and blue fills a 1×1 box. Then the hour value can be found out by adding the significance of both red and blue (since red purely indicates hour & blue has the component of both hour & minute). This is why hour value is 3+1, i.e. 4. For minutes, we must add the significance of both blue and green (since green purely indicates minutes & blue has the component of both hour & minute). This is why minute value is (5+1)x5, i.e. 30. Hence, time is 4:30.
Case 7 (Only Green) : This is only possible when the hour value is 0. However my clock coverts 0 to 12, which would have otherwise shown: 00:00, 00:05, . . . , 00:50 & 00:55. This is absolutely optional.
Note: Fibonacci clock doesn’t provide the Meridiem Indicator (i.e. AM/PM), similar to an analog clock.
Shorthand
5 squares of side lengths: 5, 3, 2, 1, 1
Red = Hour
Green = Minute x 5
Blue = Add for both (Hour) & (Minute x 5)
Empty = Ignored
Here’s the Android App
Okay, so here’s the deal. You can now download the Fibonacci Clock for Android [APK]. I’ve built this app from ground up myself, marking my first Android app (Yay!).
I’ve incorporated the manual time entry feature so that you can try, learn & master reading time on a Fibonacci clock. My favourite feature is the dock view. Can you see the ‘eye’ shaped icon on the top right? Yup, that’s for docking your Android. You can see the dock view in action in this article’s featured image (top).
Simply dock your device on a table and let the games begin. Every instance from now, solve this little puzzle to deduce the time. Double the fun by competing with your family/friends: the first to decode the clock correctly wins!
I’d love to see you try it firsthand. It was a thoroughly exciting app to work on. Wanna see how it’s done? Check the GitHub repository for Fibonacci Clock now.
It’s been quite an article, to build a solid understanding of the Fibonacci Clock. Since I wasn’t able to find an in-depth coverage of the clock across the web, I decided to make one. Do subscribe to our newsletter for more intriguing articles.
