The 4 squares problem – extended

May 1st, 2010 admin

A “4 Squares Puzzle” is doing the rounds over the internet nowadays. here are the original Microsoft Powerpoint slides which I received via email from my father. (Not sure who the original author of these slides is, but the slides report the author to be Nakit Yonetimi.) It may be useful to look over the pdf file once before proceeding. The question posted in the slides is different from the one I am going to pose, but going through the slides helps build context and helps get mentally warmed up.

The question I posed to myself after thinking through the puzzle was, “How can we divide a square into 7 equal parts with only a straight edge and a compass available?” Note that the question implies that we do not have a ruler or a scale. We have a straight edge, but without any markings on it to indicate inches or centimeters. Even if it did have the markings, such markings can only measure accurately up to a certain level. For example, say you have a scale with markings at the granularity of a millimeter. Say the square had a side equal to some irrational number, say or , or, even a simple integer which is not a multiple of 7, such as, 8 millimeters. There is no way to measure or or millimeters using such a scale.

There are at least 2 approaches to dividing this square into 7 parts. The first is a simpler approach and the second is slightly more involved. Let me talk about the second one first. The first one will then become easy to see. The main intuition behind the first idea is that a triangle’s area depends only on its base and height. If we can mark out 7 equidistant points along the square’s border, thus creating 7 equal bases, we can join the bases to the center of the square to create 7 regions with equal areas. The heights of these shapes will be equal, and the bases are equal by construction. Read the rest of this entry »

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If you cannot be a Maradona, you can certainly be a Marrow Donor

April 30th, 2010 admin

Kavita (my wife) and I recently learned about bone marrow donation, and why it is important to register with the National Bone Marrow Donor registry. Kavita registered at a drive that was being conducted at a charity event being organized in the area. Through her I came to know about SaveVinod.com. I learned that is very difficult to find a bone marrow match (1 in 100,000) and it is therefore important to keep the database of potential donors as large as possible. Further, some ethnic groups have very few listed donors – Indians (South Asians) is one such under represented group. Read the rest of this entry »

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Cool Gate-Level Logic Simulation Tool

November 14th, 2009 admin

Dr. Mark Hill of University of Wisconsin Madison pointed out the existence of this really cool learning aid to his class Logic Design class in October 2009. He also provides some guidelines about how to use the tool. Give it a shot if you like to play around with AND, OR, NOT gates and build logic. You can build “memory” structures too, something that can remember state. The following text is from Dr. Hill’s email. Enjoy. Read the rest of this entry »

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The Mathematics of Mortgage, Overpayment and Refinancing Decisions

October 7th, 2009 admin

With mortgage interest rates at historically low values refinancing home loans is an option currently being investigated by many here in the US. I, too, considered the same issue recently and discovered that this is not an easy decision to make. I developed a spreadsheet to figure out if this was a good idea. You can download this spreadsheet by clicking on this link (Microsoft Excel 2003). In general, the spreadsheet was also intended to show how loan repayment terms are set, how banks make money on loans, when overpaying monthly payments makes sense etc. Feel free to use the spreadsheet and improve upon it or tailor it to your situation. The rest of this article is a tutorial on how to make decisions about mortgages, how mortgages work in general, whether overpayment of the monthly payment makes sense, and what to consider when refinancing. The focus will be on the mathematical aspects of the decision making. Read the rest of this entry »

Posted in Experiences, Information, Tutorials | 4 Comments »

iPhone 3G Yes!

July 19th, 2009 admin

Though not an i-Phone addict yet, I am now an iPhone user. From the time I have been introduced to the iPhone, by friends, I have constantly admired the versatility and the sheer quality of the product. And after a few bad experiences with our previous phone service with Sprint we decided to switch to AT&T. It has been a relatively seamless switch. But the highlight has been the iPhone.

Even before I opened the iPhone box I was impressed with the immaculate packaging. The phone was surprisingly easy to learn using, and any non-obvious features were easy to search for on the web. The ability to download the applications of our choice and even develop your own applications is a tribute to and celebration of innovation and creativity embodied by the iPhone. I could rave about this Swiss-army knife of mobile gadgets or I could argue that no one really uses a Swiss-army knife in normal life. Indeed, I have not yet figured out how best to effectively use this phone. Some of the features that translate into time and money savings are the GPS when you are lost on the road, the ability to look up the Internet to get answers to simple questions when you are in doubt, the ability to entertain yourself when you have time to kill (books, podcasts, puzzles, YouTube, newspapers, iPod music), the ability to shoot video and ship them to your friends (thus avoiding hours of procrastination) and the ability to synchronize the contact list and calendar entries with Google. In short, this tool allows you to use small pockets of time more efficiently, either the educate or entertain yourself, or to rewind. This is important, to me at least, because then the time with family does not need to be compromised for trying to rewind in my own way. Simple example: if I feel like listening to Louis Armstrong I can listen to him and other jazz artists on Pandora while driving back from work. Then once I am home, I can spend time with Kavita, as she wants me to.

So, finally, thank you, Anu, Shankar and Sandeep, for live demos and persuasive nudges, and thanks Kavita for the final push. I’m on board and I am enjoying the ride.

(I posted this entire entry from the iPhone. I am getting very good at typing on this, something I was not so sure about only two days ago.)

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What should I do with my used PVC shower curtain liner?

July 19th, 2009 admin

When replacing the PVC shower curtain liner today, I was wondering what kind of plastic it was and whether it was recyclable.

Here is what I learnt about the various types of plastics. The following list is from Wikipedia’s article on Plastics.

1. PET (PETE), polyethylene terephthalate: Commonly found on 2-liter soft drink bottles, water bottles, cooking oil bottles, peanut butter jars.
2. HDPE, high-density polyethylene: Commonly found on detergent bottles, milk jugs.
3. PVC, polyvinyl chloride: Commonly found on plastic pipes, outdoor furniture, siding, floor tiles, shower curtains, clamshell packaging.
4. LDPE, low-density polyethylene: Commonly found on dry-cleaning bags, produce bags, trash can liners, and food storage containers.
5. PP, polypropylene: Commonly found on bottle caps, drinking straws, yogurt containers, Lego building blocks.
6. PS, polystyrene: Commonly found on “packing peanuts”, cups, plastic tableware, meat trays, take-away food clamshell containers
7. OTHER, other: This plastic category, as its name of “other” implies, is any plastic other than the named #1–#6, Commonly found on certain kinds of food containers, Tupperware, and Nalgene bottles.

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Have people forgotten Shiva?

July 19th, 2009 admin

Hinduism has a notion of trinity – three forces that drive the universe. The trinity consists of the creator, the sustainer and the destroyer (personified respectively by Brahma, Vishnu and Shiva). I do not claim to know the spiritual aspect of this concept. However, the applicability of this concept to the physical things in our lives is almost obvious. Everything physical comes into being, serves its purpose during its lifetime and is (or rather, should be) eventually destroyed. These three forces must guide each other in an eternal cycle, rather than in a linear progression. That which is destroyed, must contribute to the creation, and that which is created must be destroyable. This is not philosophy; this is just the principle of equilibrium and balance. Read the rest of this entry »

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A Fleeting Experience

December 26th, 2008 admin

We are driving towards Orlando in our overloaded Pontiac Vibe. Anant is in the driver’s seat; Kavita is sitting behind him, with a mountain of boxes and bags filled with camping stuff, food, clothes, maps, cameras and stuff for our week-long road trip almost leaning onto her to her right and from behind her. We are listening to Ira Glass’s “This American Life” CD. Up until a few minutes ago, I was reading the New Yorker magazine that Anant had brought with him from California. But as the light outside faded, I could not read any more and my mind wandered. Read the rest of this entry »

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Anekantavada – Multiplicity of viewpoints

September 19th, 2008 admin

I opened wikipedia by chance this morning and the very first article I saw was on Anekantavada, a concept from Jain Philosophy, which observes and explains that there is always multiplicity of view points when trying to comprehend any truth. Limited, partial or conditional view points can lead to different interpretations of any truth. It is therefore important to respect the existance of other view points, while at the same time recognizing the fallibility of your own. Apparently the story of the blind men and the elephant is often used to explain this concept. This struck me as fascinating because only a few months back, I had used the same example to reach an almost identical philosophy! This philosophy may also help us understand the underlying meaning behind the millions of Gods that some religions accept – the acceptance of the existance of those millions of view points.

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Sandeep’s New Rating System

September 17th, 2008 admin

Sandeep Somani came up with this scheme of rating TV shows, movies, plays etc. It takes away the relative interpretation and quantization associated with stars, and instead gets to the meat of the matter with an absolute measure in terms of the dollar value you are willing to pay to see the show/movie etc. To add to your ability to express your dissatisfaction you may also choose to quote how much money you will need to be paid, to go see the show. Read the rest of this entry »

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