Know : Grow and Shrink inside an Ames Room

Do you know how the normal sized humans transformed as Hobbits in the movie The Lord Of The Rings? You too can shrink and grow back as they did 🙂 Because they used several Ames room sets in Shire sequences to make the heights of the diminutively-sized hobbits correct when standing next to the taller Gandalf.

What is an Ames Room? Well before getting into the detailing watch this video by The Royal Institution

A diagram of the true and apparent position of a person in an Ames room, and the shape of that room

An Ames room is a distorted room that is used to create an optical illusion. Probably influenced by the writings of Hermann Helmholtz, it was invented by American ophthalmologist Adelbert Ames, Jr. in 1934, and constructed in the following year.

An Ames room is constructed so that from the front it appears to be an ordinary cubic-shaped room, with a back wall and two side walls parallel to each other and perpendicular to the horizontally level floor and ceiling. However, this is a trick of perspective and the true shape of the room is trapezoidal: the walls are slanted and the ceiling and floor are at an incline, and the right corner is much closer to the front-positioned observer than the left corner (or vice versa). (See overhead view diagram to the right)

As a result of the optical illusion, a person standing in one corner appears to the observer to be a giant, while a person standing in the other corner appears to be a dwarf. The illusion is so convincing that a person walking back and forth from the left corner to the right corner appears to grow or shrink.

Studies have shown that the illusion can be created without using walls and a ceiling; it is sufficient to create an apparent horizon (which in reality will not be horizontal) against an appropriate background, and the eye relies on the apparent relative height of an object above that horizon.

Courtesy : The Royal Institution via YouTube, Wikipedia

Know : Triangle, Square, Pentagon… How long it goes?

Triangle Δ (3), Square (4), Pentagon (5), Hexagon (6), Heptagon(7), Octagon(8)… How long it can go?

A Megagon is a shape with 1,000,000 equal sides.  Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.

regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). 

How many you know before? How to draw a perfect polygon with 10 sides? Know more here… (To see how to draw them? Scroll down the table)

Number of sides Name of polygon Picture
n Regular n-gon
3 Equilateral Triangle  Triangle.Equilateral.svg
4 Square  Regular polygon 4 annotated.svg
5 Regular Pentagon  Regular polygon 5 annotated.svg
6 Regular Hexagon  Regular polygon 6 annotated.svg
7 Regular Heptagon  Regular polygon 7 annotated.svg
8 Regular Octagon  Regular polygon 8 annotated.svg
9 Regular Nonagon  Regular polygon 9 annotated.svg
10 Regular Decagon Regular polygon 10 annotated.svg 
11 Regular Hendecagon  Regular polygon 11 annotated.svg
12 Regular Dodecagon  Regular polygon 12 annotated.svg
13 Regular Tridecagon  Regular polygon 13 annotated.svg
14 Regular Tetradecagon Regular polygon 14 annotated.svg 
15 Regular Pentadecagon  Regular polygon 15 annotated.svg
16 Regular Hexadecagon  Regular polygon 16 annotated.svg
17 Regular Heptadecagon Regular polygon 17 annotated.svg 
18 Regular Octadecagon  Regular polygon 18 annotated.svg
19 Regular Enneadecagon Regular polygon 19 annotated.svg 
20 Regular Icosagon  Regular polygon 20 annotated.svg
100 Regular Hectagon Internal Angle 176.40°External Angle 3.60°
1000 Regular Chiliagon  Chiliagon.pngA whole regular chiliagon is not visually discernible from a circle. The lower section is a portion of a regular chiliagon, 200 times as large as the smaller one, with the vertices highlighted.Internal Angle = 179.64°
10000 Regular Myriagon  Internal Angle = 179.96°
1,000,000 Regular Megagon  Circle - black simple.svgEven if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.Internal Angle = 179.99964°

Geometric Construction of Regular Polygons

Equilateral Triangle Inscribed in a Circle.gif

Equilateral triangle


File:Straight Square Inscribed in a Circle 240px.gif



File:Regular Pentagon Inscribed in a Circle 240px.gif





Approximated Heptagon Inscribed in a Circle.gif



File:Regular Octagon Inscribed in a Circle.gif



Approximated Nonagon Inscribed in a Circle.gif



Construction of a regular decagon



Costruzione approssimata dell'endecagono regolare



Regular Dodecagon Inscribed in a Circle.gif



File:Approximated Tridecagon Inscribed in a Circle.gif



Approximated Tetradecagon Inscribed in a Circle.gif



Regular Pentadecagon Inscribed in a Circle.gif



Regular Hexadecagon Inscribed in a Circle.gif



Regular Heptadecagon Using Carlyle Circle.gif







Regular Icosagon Inscribed in a Circle.gif


Courtesy : Wikipedia ( All copyrights of the above images and animations belongs to the respective owners as mentioned in Wikipedia, shared here for educational purposes only)

Tribute : Shakuntala Devi “Human Computer”



In 1977 in USA she competed with a computer to see who gives the cube root of 188,132,517 faster, she won. That same year, at the Southern Methodist University she was asked to give the 23rd root of a 201-digit number; she answered in 50 seconds. Her answer—546,372,891—was confirmed by calculations done at the U.S. Bureau of Standards by the Univac 1101 computer, for which a special program had to be written to perform such a large calculation.

On June 18, 1980, she demonstrated the multiplication of two 13-digit numbers 7,686,369,774,870 × 2,465,099,745,779 picked at random by the Computer Department of Imperial College, London. She correctly answered 18,947,668,177,995,426,462,773,730 in 28 seconds. This event is mentioned in the 1982 Guinness Book of Records.

Shakuntala Devi (November 4, 1929 – April 21, 2013), popularly known as the “Human Computer”, was a child prodigy and mental calculator. Her talents earned her a place in the 1982 edition of The Guinness Book of World Records.

Google, on Monday Nov.4,2013, celebrated mathematics wizard Shakuntala Devi’s 84th birthday with a doodle. 

Shakuntala Devi was born in Bangalore, India, to an orthodox Kannada Brahmin family. Her father rebelled against becoming a temple priest and instead joined a circus where he worked as a trapeze artist, lion tamertightrope walker and magician. Devi’s father discovered her ability to memorize numbers while teaching her a card trick when she was about three years old. Her father left the circus and took her on road shows that displayed her ability at number crunching. She was able to do this without any formal education. By age six she demonstrated her calculation and memorization abilities at the University of Mysore.

In 1944 Devi moved to London with her father. She returned to India in the mid-1960s and married Paritosh Bannerji, an officer of the Indian Administrative Service from Kolkata. She and her husband were divorced in 1979. Devi returned to Bangalore in the early 1980s.

Devi travelled the world demonstrating her arithmetic talents, including a tour of Europe in 1950 and a performance in New York in 1976. In 1988 she returned to the US to have her abilities studied by Arthur Jensen, a professor of psychology at the University of California, Berkeley. Jensen tested her performance at several tasks, including the calculations of large numbers; Examples of the problems presented to Devi were calculating the cube root of 61,629,875, and the seventh root of 170,859,375. Jensen reported that Devi was able to provide the solution to the aforementioned problems (the answers being 395 and 15 respectively) before Jensen was able to copy them down in his notebook. Jensen published his findings in the academic journal Intelligence in 1990.

In addition to her work as a mental calculator, Devi was an astrologer and an author of several books, including cookbooks and fictional novels.


Courtesy : Google and Wikipedia