Archive for November, 2010
A lot of people were made a bit uncomfortable when they saw the new Windows Phone 7 start screen and it’s long area of blank space on the right side. What’s with the wasted space? The offset grid and negative space are clearly by design. The key phrase there is "by design." This isn’t your average boring grid of program icons that every other smartphone employs in their user interface designs. The layout actually follows many design conventions that artists, mathematicians, and scientists have developed over centuries.
The Rule of Thirds
Anyone who’s ever taken a photography class knows about the rule of thirds. If you draw grid lines at both one-third increments between the horizontal and vertical lengths of the frame, the intersections of those lines are where you want to place your subject. The idea is that placing your subject in the center of the frame makes the composition too symmetric and thus bland and uninteresting. Having the subject off-center gives you room for your eye to wander with curiosity. The negative space of an off-center composition actually brings balance to the image while also adding interest and excitement.
The Windows Phone 7 start page design does not adhere to a straight-symmetric grid of equal-weight icons like most other smartphone platforms do. The off-center grid puts importance on the Live Tiles, while the negative space on the right balances the composition.
The classical composition technique of divine proportions is a little more complex than the rule of thirds. Throughout history, divine proportions have been used to evoke emotion or aesthetic feelings within humans. The concept is often also referred to as the Golden Mean, the Magic Ratio, the Golden Ratio, the Fibonacci Series, etc. It’s even extremely prominent in nature. You’ll see divine proportions in galaxy formations, seashells, growth patterns of plants, the breeding of rabbits, and plenty of other places.
Artists like Michelangelo, Raphael, and Leonardo da Vinci take into account the divine proportions all the time. Your designs don’t have to follow the proportions exactly, but using them as guides is sure to increase the aesthetics.
When we overlay a divine proportions spiral with the Windows Phone 7 start screen, you’ll see the spiral clearly flows through the negative space surrounding the top and right areas, and then focuses in on the top left tile. That’s where your eye is going to go and that’s where you should arrange your most important Live tile.
See Wikipedia for more about divine proportions.
The off-center design even has some functional advantages. Like many people, I normally hold my phone in my left hand leaving my right hand to touch the screen or carry bags or do something else. While holding a Windows Phone 7 device in your left hand, the live tiles are closer to that side. This makes it easier to one-handedly flick through the list and get to the information that you want.
Then when you’re in the tile-arrangement mode, there needs to be a way to cancel the mode and get back to the normal start screen. Tapping the empty area on the right is a good way to do that. Lastly, of course, there needs to be some room for that little arrow that shows the user that if they press there or swipe that way they’ll get more stuff… namely the programs listing.
Fibonacci Numbers (The source of the Devine Proportion)
The sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, … (each number is the sum of the previous two).
The ratio of successive pairs is so-called golden section (GS) – 1.618033989 . . . . .
whose reciprocal is 0.618033989 . . . . . so that we have 1/GS = 1 + GS.
The Fibonacci sequence, generated by the rule f1 = f2 = 1 , fn+1 = fn + fn-1,
is well known in many different areas of mathematics and science.
Pascal’s Triangle and Fibonacci Numbers
The triangle was studied by B. Pascal, although it had been described centuries earlier by Chinese mathematician Yanghui (about 500 years earlier, in fact) and the Persian astronomer-poet Omar Khayyám.
Pascal’s Triangle is described by the following formula:
where is a binomial coefficient.
The "shallow diagonals" of Pascal’s triangle
sum to Fibonacci numbers.
It is quite amazing that the Fibonacci number patterns occur so frequently in nature
( flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal "laws of nature". Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone. In addition, numerous claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, and the curve of waves The Fibonacci numbers are also found in the family tree of honeybees.
Fibonacci and Nature
Plants do not know about this sequence – they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.
Why do these arrangements occur? In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space. This is well described in several books listed here >>
So nature isn’t trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect.
The plant is responding to physical constraints, not to a mathematical rule.
The basic idea is that the position of each new growth is about 222.5 degrees away from the previous one, because it provides, on average, the maximum space for all the shoots. This angle is called the golden angle, and it divides the complete 360 degree circle in the golden section, 0.618033989 . . . .
Examples of the Fibonacci sequence in nature.
Petals on flowers*
Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, we would find that the number of petals on a flower, that still has all of its petals intact and has not lost any, for many flowers is a Fibonacci number:
- 3 petals: lily, iris
- 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia)
- 8 petals: delphiniums
- 13 petals: ragwort, corn marigold, cineraria,
- 21 petals: aster, black-eyed susan, chicory
- 34 petals: plantain, pyrethrum
- 55, 89 petals: michaelmas daisies, the asteraceae family
Some species are very precise about the number of petals they have – e.g. buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.
white calla lily
Two-petalled flowers are not common.
Three petals are more common.
Five petals – there are hundreds of species, both wild and cultivated, with five petals.
Eight-petalled flowers are not so common as five-petalled, but there are quite a number of well-known species with eight.
Twenty-one and thirty-four petals are also quite common. The outer ring of ray florets in the daisy family illustrate the Fibonacci sequence extremely well. Daisies with 13, 21, 34, 55 or 89 petals are quite common.
shasta daisy with 21 petals
Ordinary field daisies have 34 petals …
a fact to be taken in consideration when playing "she loves me, she loves me not". In saying that daisies have 34 petals, one is generalizing about the species – but any individual member of the species may deviate from this general pattern. There is more likelihood of a possible under development than over-development, so that 33 is more common than 35.
* Read the entire article here:
Flower Patterns and Fibonacci Numbers
Why is it that the number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34 or 55? For example, the lily has three petals, buttercups have five of them, the chicory has 21 of them, the daisy has often 34 or 55 petals, etc. Furthermore, when one observes the heads of sunflowers, one notices two series of curves, one winding in one sense and one in another; the number of spirals not being the same in each sense. Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? The same for pinecones : why do they have either 8 spirals from one side and 13 from the other, or either 5 spirals from one side and 8 from the other? Finally, why is the number of diagonals of a pineapple also 8 in one direction and 13 in the other?
© All rights reserved Image Source >>
Are these numbers the product of chance? No! They all belong to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (where each number is obtained from the sum of the two preceding). A more abstract way of putting it is that the Fibonacci numbers fn are given by the formula f1 = 1, f2 = 2, f3 = 3, f4 = 5 and generally f n+2 = fn+1 + fn . For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that one understands why. It is a question of efficiency during the growth process of plants.
The explanation is linked to another famous number, the golden mean, itself intimately linked to the spiral form of certain types of shell. Let’s mention also that in the case of the sunflower, the pineapple and of the pinecone, the correspondence with the Fibonacci numbers is very exact, while in the case of the number of flower petals, it is only verified on average (and in certain cases, the number is doubled since the petals are arranged on two levels).
We have covered free tools like Skydrive Explorer and also Gladinet which can help you to access Windows Live Skydrive as a network drive. If you do not want to use a third party tool to access Windows Live Skydrive, you can still map it as a network drive and access any folder in Skydrive. For mapping Skydrive to Windows Explorer, we are using the SSL connection and for this we need the unique ID (WebDAV access) for connecting which can be obtained using a small portable tool.
1. First step is to get the WebDAV access address for your Skydrive account. For this there is a simple portable tool called SkyDrive Simple Viewer. Run the tool and login to your Skydrive and select the folder which you want to map.
In the image above, you can see an address corresponding to the folder I have selected. The address looks like this-
Here the sdfsd24645759 refers to the path which is the same as a personal sub domain when logging on to SkyDrive the normal way from your web browser. It can look like “http://cid-sdfsd24645759.skydrive.live.com/”. The sub domain cdckda refers to the your account and the folder you are trying to access.
2. Next step you need to make some modification to the URL.
The original URL- https://cdckda.docs.live.net/sdfsd24645759/Documents
Modified URL- \\cdckda.docs.live.net@SSL\sdfsd24645759\Documents
We are connecting using the SSL for Windows Live Skydrive.
3. Open Windows Explorer, right click on the Network and select Map Network Drive.
4. In the Map Network Drive option, enter the folder as \\cdckda.docs.live.net@SSL\sdfsd24645759\Documents. You can also chose to reconnect at Login and if you want to connect using multiple account, check the second box as well.
5. It will prompt you to enter the Windows Live credentials after attempting to connect to Skydrive.
Now the network drive will be connected and you can see the drive in Window Explorer.