"Which way did the bicycle go?"

Problem: If you are given the plot of the tracks traced by the front and rear wheel of the bicycle, how will you tell which direction the bicycle was going? For e.g. consider these two figure


In these two figures, how would you decide which direction the bicycle was going i.e. right to left or left to right ? What would be the idea or basis behind your method ?

I came across this problem while reading the book "Which way did the bicycle go? and other intriguing mathematical mysteries" by Joseph D. E. Konhauser, Dan Velleman and Stan Wagon, published by the Mathematical Association of America. As mentioned in the preface of this book, it is a collection of some 190 problems taken from the "Konhauser collection". The problems are grouped under six main topics (plane geometry, number theory, algebra, combinatorics and graph theory, three-dimensional geometry, and miscellaneous) each of which has further sub-groups.

As for the level of mathematics needed, I have not gone through the full book but based on the problems which I have read, I think mathematics up to 12th standard might be enough. Get the book and have fun solving problems.

Making part of the image black and white in Gimp

Here is a way of making a part of the image B&W in Gimp. The basic idea is to select the portion which we want to change and while keeping it selected, make the changes. In case the part which needs the change is the major portion, it might be easy to select the rest of the portion and then invert the selection. Here I will let the speed and roundabout sign in yellow remain as it is and make changes to the rest of the figure.

(1) Open the image in Gimp

(2) Select the "zoom" tool

(3) Zoom-in on the yellow sign by repeatedly clicking on it

(4) Select the "path" tool

(5) Using the path tool draw the outline of the yellow sign. You will notice that as you click, small circles will be made at the point where you click. Also, the latest point is connected to the previous one making a "path". In order to end or close the path, after you have gone all around the sign, click on the very first circle.


(6) Now from the "select" menu click on "from path"

(7) When you do so the circles and dash line made by the path tool will all be connected, and you have a dash (moving ant like) line on the outline of the yellow sign.

(8) From the "select" menu click on "invert". As of now everything inside the path is selected, with "invert" everything outside the current selection will be selected.

(9) Use the zoom tool to zoom-out to see the full image.

(10) From the "color" menu select "desaturate"

(11) In the picture everything except for the yellow sign will turn B&W. Also you will be presented with three options of how to desaturate. You can click on each and see which you like best.

(12) Now that its B&W, for a final touch we can adjust the contrast. To do so, from the "color" menu select "brightness and contrast".

(13) Use the slider to increase the contrast to the level you want.

(14) Finally, from the "select" menu click on "none" to remove any current selections.

(15) Now that its done, it may be saved in this final version.

There are other methods of doing this but for this image I think this is the simplest way.

The dust particle that occupied my mind

First the story of how the dust particle appeared

On Sunday it snowed. The first of this season. In the evening it was pretty cold but had almost stopped snowing. I had plans to go to my friends place and decided to take along my Nikon-D40. Just as I was about to leave, plans for making a snow man came up and the next hour was devoted to making it. During that fun time I took several pictures. Later at my friends place I took out my camera to show what I had been doing for the last hour. The pictures looked good. But I realized that since it was pretty warm inside and the camera had been outside for a long time (though in the bag mostly) moisture was beginning to appear on the UV filter and on the view-finder. I used the lens cleaning cloth to wipe the moisture off.

That is when I looked though the view-finder and found that I could see a spot in the lower right corner. I wiped the view-finder and the UV filter again, but still the spot was there. So I took a couple of pictures of the bare walls and found that in the picture I could see a clear spot in the middle.

What might have happened

Since I could see a spot in the view-finder and also in the final picture (and I tested that with two lens) it seemed that maybe I had some dust particles on the mirror (view-finder) and also on the sensor (final picture). I was ok with spots in the view finder, but not so ok with them being there in the final picture.

Testing for dust particles on the sensor

This is what I read on the internet. So credits to whose ever article I read that time. I don't remember the exact advise and reasoning but this is essentially what I did after reading that page.

(1) Set the focal length to maximum.
(2) Set the aperture to minimum.
(3) Set the focus (manual) completely off.
(4) Take a picture of a blank white sheet.
(5) Look at the picture and check for black/grey spots.

In my case, I could anyway see the spot in the final pictures, but when I did this then the spot was more prominent.

The solution: Blow air and clean the sensor/filter

Long story short here is how the spot in the final picture was removed.

(1) Things needed - Camera, air blower, enough light to look at the sensor/filter area.
(2) Better to have a fully charged battery.
(3) Remove the lens from the camera body.
(4) Turn the camera on and from the setup menu set the "Mirror lock-up" option to "On".
(5) Set the camera mode to manual.
(6) Change the shutter speed till you reach the "Bulb" mode.
(7) Now press the shutter button and keep it pressed.
(8) The mirror will give way to the sensor/filter area.
(9) Look at the sensor/filter surface. In my case I could clearly see a speck of dust in the center of the surface.
(10) Use the air blower and blow air on the sensor/filter area while holding the camera upside down (so that dust can easily fall vertically down).
(11) Release the shutter button.
(12) Switch the camera off.
(13) Put back the lens, take some pictures and see if it helped.

Needless to say that this is what I did and its better that you read your manual and decide what to do.

Happy clicking.

Book list

I keep posting post-its on my desktop screen (not the paper ones ... there is also a software) on which many a times I note down the name of books which I came across, was told about by some friend etc. etc. Many a times I don't use the post-it software but rather note the things down in a text document. So now I thought lets make use of the blog to keep track of these things. There is no specific ordering here.

--------------------
Fiction/Non-fiction
--------------------

• J. Heine and J-P. Praderes (2005) "The golden age of hand-built bicycles"
  
• S. Wolpert (2000) "A new history of India"
• B. Russell (1968 first, 1995 revised edition) "Unpopular essays"
  
• Greg Mortenson and David Oliver Relin (2007) "Three cups of tea".
• C. K. Prahalad (2005) "Fortune at the bottom of the pyramid".
• J. Diamond (1999) "Guns germs and steel - the fates of human societies"
• A. Adiga (2008) "The white tiger"
• M. Gladwell (2008) "Outliers - the story of success"
• M. Gladwell (2005) "Blink - the power of thinking without thinking"
  
• J. B. Taylor (2009) "My stroke of insight - a brain scientist's personal journey"
• A. Levitsky (2008) "Worlds apart an anthology of Russian fantasy and science fiction"
• J. Krause (2008) "Photo idea index - places"
• T. Ang (2008) "Digital photography masterclass"

-----------------------
Science/History/Etc.
-----------------------

• William Dunham (1990) "Journey through genius: the great theorems of mathematics" (This is a keeper)
• J. Kakalios (2006) "The physics of superheroes" (Great for introductory physics and makes me want to read comic books)
• M. Hoagland and B. Dodson (1999) "Patterns - sixteen things you should know about life"
• B. Bryson (2003) "A short history of nearly everything"
• C. Sagan (1997) "Billions and billions"
  
• S. Hawking and L. Mlodinow. () "Briefer history of time"
• P. Atkins (2003) "Galileo's finger : the ten great ideas of science"
• George Pólya (1962) "Mathematical discovery; on understanding, learning, and teaching problem solving".
• George Pólya (1954) "Mathematics and plausible reasoning".
• F. Hidetoshi and T. Rothman (2008) "Sacred mathematics - Japanese temple geometry"
• Martin Aigner, Günter M. Ziegler (2003) "Proofs from THE BOOK".
• (2004) "Sherlock Holmes in Babylon : and other tales of mathematical history"
• Frank E Burk (2007) "A Garden of Integrals"
• C. Alsina and R Nelsen (2009) "When less is more: Visualizing basic inequalities"
• M. Levi (2009) "The mathematical mechanic: Using physical reasoning to solve problems"
• J. A. Adam (2009) "A mathematical nature walk"
• J. Bryant and C. Sangwin (2008) "How round is your circle? Where engineering and mathematics meet"
• S. Kalajdzievski (2008) "Math and art - an introduction to visual mathematics"
• M. Hoagland and B. Dodson (1998) "The way life works - The science lover's illustrated guide to how life grows, develops, reproduces, and gets along"
• D. E. Smith () "A source book in mathematics"

--------------------
Science puzzles etc.
--------------------

• W. W. R. Ball (1939) "Mathematical recreations and essays"
• A. H. Beiler (1966) "Recreations in the theory of numbers : the queen of mathematics entertains"
• J. D. E. Konhauser, D. Velleman and S. Wagon (1996) "Which way did the bicycle go? and other intriguing mathematical mysteries"
• K. Kendig (2008) "Sink or float? Thought problems in math and physics"
• L. Weinstein and J. A. Adam (2008) "Guesstimation - solving the world's problems on the back of a cocktail napkin"
• R. Honsberger (2004) "Mathematical delights"
• R. Honsberger (2003) "Mathematical diamonds"
• R. Honsberger (1991) "More mathematical morsels"
• J. Havil (2008) "Impossible? surprising solutions to counter-intuitive conundrums"
• J. Martineau (2002) "A little book of coincidence"

Song info - 순정만화 (Hello Schoolgirl)

Movie - 순정만화 (Hello Schoolgirl)

There is a song in this movie which plays in the background while Ha-kyeong and Sook are having dinner for the first time in the restaurant right after they catch the last train. The song remains in the background while Ha-kyeong and Sook are talking and comes in the foreground for maybe 10 seconds. I wanted to know which song this was and finally with the help of some friends I was able to find it. The song is "바이러스 - 이영진" or "Virus - Lee Young-Jin". It is not listed in the OST of this movie but can be found in the listing of the OST of "Crazy Waiting".

Also, some have asked about the song which plays in the trailer for this movie. That song can be found in Youtube by looking up - Minusul 100% romantic - it will be the first result.

I forgot I had opened an account here

I just now realized that at some point in time I had opened an account on Blogger. As I had then suspected this blog of mine has almost died. I find it easier to upload pictures on Picasa and Flickr than to type here. Though the initial plan was to even post pictures here with some explanations as to why I took them and what was the idea I had in mind. Lets see if that can be done.

Here is the link to an article I came across on "The New Yorker" titled "How David Beats Goliath" :
http://www.newyorker.com/reporting/2009/05/11/090511fa_fact_gladwell

Hibernation option when you click "Turn Off Computer"

Operating system (which I use): Windows XP Professional

Issue: When I go to the "Start" button and click on "Turn Off Computer" I see three options, "Stand By" "Turn Off" and "Restart". If I'm at this screen its always to turn the computer off, but where is the hibernation option ? I do have "Enable hibernation" checked in the power options.

Solution: Press the "Shift" key and the "Stand By" option will change to "Hibernate".