Snapshots from the VR project display
for Endoscopy simulation
using Samsung Gear VR
Sunday, 31 January 2016
Monday, 25 January 2016
bolg on various ways to represent numbers
Representation of numbers in various
other ways
Numbers : Objects
which enable us to count , measure , label other entities.
Major classifications of
number can be made from this diagram :
a)
Natural numbers
b)
Whole numbers
c)
Integers
d)
Rational numbers
e)
Irrational numbers
f)
Complex numbers.
1. ASCII Art Generator
This generates the shape of numbers using { / , ‘ , . , - , _ , = }
Source :
2. Turning Numbers into pictures
Turning Numbers into pictures of well know items for better memorization while making a list of items. This is a technique is used to increase memory power by representing numbers as items seen in day to day life which can be used to make a story line around the other objects thus creating a network in which each item is linked to another . Hence just by remembering the Story line (which is easy to remember than random words) you remember everything.
Here are the representations:
1
2
3
4
5
6
7
8
9
10
Source:
http://www.slideshare.net/speed-reading/how-to-turn-numbers-into-images-to-remember-a-list-of-anything-14193729
3. Numbers to Bar-codes
The UPC system
encodes only the manufacturer's identity and an identification number for the
specific product. There is nothing to gain by attempting to read the barcode
yourself. Instead, look it up online using free services such as GTIN's, the official U.S.
bar code assignment company, or upcdatabase.org,
which is a database created by users.
4. Sounds of Pi (π) – way of representing pi through music.
Source : https://www.youtube.com/watch?v=wPn4tgmU8ek
From time 2:35 mins in the video , Professor Philip Moriarty shows the demonstration on guitar .
Idea: Take the numbers and mapped those to C major scale of electric guitar so that:
1 is c ,
2 is d ,
3 is e
and so on until 9 and then 0.
5. Pi and Buffon's Matches Experiment
It’s an experiment with an amazing result.
Experiment goes as follows :
Step 1. Take a plane drawing sheet and draw equally spaced horizontal lines on it. Space between the lines should be equal to the twice of the size of match sticks that you are going to use.
Step 2. Take bunch of match Sticks (say 500) and drop them randomly over the drawing sheets.
Step 3. Count the Number of match sticks which crosses the horizontal line and let’s call it Ncrossing where Ntotal was 500 ( you can take lager sample for better accuracy ).
Result : (Ntotal / Ncrossing) = 3.14 { approx. }
Source: https://www.youtube.com/watch?v=sJVivjuMfWA
6. Pi and the Bouncing ball Experiment .
Its an
interesting thought experiment assuming perfectly elastic collision which means
that when a bodies collide their kinetic energy and momentum are conserved.
Experiment
:
Step 1 : Take two
Balls of different sizes and mass .
Step 2 : Consider
Mass of bigger Ball to be ‘M’ and smaller ball to be ‘m’
Step 3 : Keep the
smaller ball in between bigger ball and a wall.
Step 4 : Give the bigger
ball a velocity ‘V’ towards the smaller ball.
Mass of
the bigger ball = M
Mass of
the smaller ball = m
Given relation : M = (16 x 100N
) x m //N is any natural number ; eg:
1,2,3..
Observation
: As a result of collision the smaller ball rolls off to hit the wall. Because of
elastic collision (as we have assumed) it gets bounced off the wall and now
starts moving towards the bigger ball. Meanwhile the bigger ball is carrying on
to move closer towards the wall. Collision between them (small and big ball)
occurs again , where little bit of smaller ball’s momentum is imparted on the
bigger ball thus slowing it down and causing itself to bounce off again towards
the wall. This keeps on happening and eventually the big ball slows down enough
that with the next collision it will change its directions entirely and will
start going backwards (i.e away from the wall )
Question :
how many collision between the balls took place before the bigger ball changed
its direction ?
Answer : Number of collision = (N+1) characters of π
7. Complex Numbers representation via Fractals.
We can generate beautiful art from complex numbers. These designs are called fractals. Fractals are produced using an iteration process. This is where we start with a Complex number and then feed it into a formula. We get a result and feed this result back into the formula, getting another result. And so on and so on.
Common fractals are based on the Julia Set
Julia Set
The Julia Set equation is:
Zn+1
= (Zn)2 + c
For the Julia Set, the value of
Example of a Julia Set:
If we start with the complex number Z1= 0.5 + 0.6j, and let c = 0.3
Z2 = (0.5 + 0.6j)2 + 0.3 = 0.19 + 0.6j
so on …
Z2 = (0.5 + 0.6j)2 + 0.3 = 0.19 + 0.6j
so on …
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