Thursday, October 29, 2009

Beauty of Mathematics

Here are some funny math interesting facts. All the below tricks are based around the sequential manipulation of the numbers being used for input and output.

Sequential Inputs of numbers with 8
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Sequential 1's with 9
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 + 10 = 1111111111

Sequential 8's with 9
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Numeric Palindrome with 1's
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

Without 8
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999

Sequential Inputs of 9
9 x 9 = 81
99 x 99 = 9801
999 x 999 = 998001
9999 x 9999 = 99980001
99999 x 99999 = 9999800001
999999 x 999999 = 999998000001
9999999 x 9999999 = 99999980000001
99999999 x 99999999 = 9999999800000001
999999999 x 999999999 = 999999998000000001
......................................

Sequential Inputs of 6
6 x 7 = 42
66 x 67 = 4422
666 x 667 = 444222
6666 x 6667 = 44442222
66666 x 66667 = 4444422222
666666 x 666667 = 444444222222
6666666 x 6666667 = 44444442222222
66666666 x 66666667 = 4444444422222222
666666666 x 666666667 = 444444444222222222
......................................

Posted via email from Edward Anil's Blog

Friday, July 03, 2009

SixthSense - wearable gestural interface

We've evolved over millions of years to sense the world around us. When we encounter something, someone or some place, we use our five natural senses to perceive information about it; that information helps us make decisions and chose the right actions to take. But arguably the most useful information that can help us make the right decision is not naturally perceivable with our five senses, namely the data, information and knowledge that mankind has accumulated about everything and which is increasingly all available online. Although the miniaturization of computing devices allows us to carry computers in our pockets, keeping us continually connected to the digital world, there is no link between our digital devices and our interactions with the physical world. Information is confined traditionally on paper or digitally on a screen. 

SixthSense bridges this gap, bringing intangible, digital information out into the tangible world, and allowing us to interact with this information via natural hand gestures. ‘SixthSense’ frees information from its confines by seamlessly integrating it with reality, and thus making the entire world your computer.

The SixthSense prototype is comprised of a pocket projector, a mirror and a camera
The hardware components are coupled in a pendant like mobile wearable device.
Both the projector and the camera are connected to the mobile computing device in the user’s pocket. 
The projector projects visual information enabling surfaces, walls and physical objects around us to be used as interfaces; while the camera recognizes and tracks user's hand gestures and physical objects using computer-vision based techniques.

The software program processes the video stream data captured by the camera and tracks the locations of the colored markers (visual tracking fiducials) at the tip of the user’s fingers using simple computer-vision techniques. 
The movements and arrangements of these fiducials are interpreted into gestures that act as interaction instructions for the projected application interfaces.
The maximum number of tracked fingers is only constrained by the number of unique fiducials, thus SixthSense also supports multi-touch and multi-user interaction.

   

The SixthSense prototype implements several applications that demonstrate the usefulness, viability and flexibility of the system. 
  • The map application lets the user navigate a map displayed on a nearby surface using hand gestures, similar to gestures supported by Multi-Touch based systems, letting the user zoom in, zoom out or pan using intuitive hand movements. 
  • The drawing application lets the user draw on any surface by tracking the fingertip movements of the user’s index finger. 
  • SixthSense also recognizes user’s freehand gestures (postures). For example, the SixthSense system implements a gestural camera that takes photos of the scene the user is looking at by detecting the ‘framing’ gesture. The user can stop by any surface or wall and flick through the photos he/she has taken. 
  • SixthSense also lets the user draw icons or symbols in the air using the movement of the index finger and recognizes those symbols as interaction instructions. For example, drawing a magnifying glass symbol takes the user to the map application or drawing an ‘@’ symbol lets the user check his mail. 
  • The SixthSense system also augments physical objects the user is interacting with by projecting more information about these objects projected on them. For example, a newspaper can show live video news or dynamic information can be provided on a regular piece of paper. 
  • The gesture of drawing a circle on the user’s wrist projects an analog watch.
Pranav Mistry is the genius behind Sixth Sense, a wearable device that enables new interactions between the real world and the world of data.
Pranav Mistry is a PhD student in the Fluid Interfaces Group at MIT's Media Lab. Before his studies at MIT, he worked with Microsoft as a UX researcher. Mistry is passionate about integrating the digital informational experience with our real-world interactions.

Some previous projects from Mistry's work at MIT includes intelligent sticky notes, Quickies, that can be searched and can send reminders; a pen that draws in 3D; and TaPuMa, a tangible public map that can act as Google of physical world. His research interests also include Gestural and Tangible Interaction, Ubiquitous Computing, AI, Machine Vision, Collective Intelligence and Robotics.

Posted via email from Edward Anil's Blog