100.000th blog view expected on 11/11/11

This blog has had close to 100,000 page views since August 2008 and it looks like that the 100,000th page will be viewed on 11/11/11. This is a coincidence, of course. But with all the hype surrounding 11/11/11 I thought I should mention it. - Another example of the NumerologyIsNotMathematics principle. ;-)

EDIT:
( Although not 11/11-'11 yet on all parts of the world. )

Practical geometry

Geometry originated as a practical science concerned with surveying, measurements, areas, and volumes. Among the notable accomplishments one finds formulas for lengths, areas and volumes, such as Pythagorean theorem,circumference and area of a circle, area of a triangle, volume of a cylinder, sphere, and a pyramid. A method of computing certain inaccessible distances or heights based on similarity of geometric figures is attributed to Thales. Development ofastronomy led to emergence of trigonometry and spherical trigonometry, together with the attendant computational techniques.

Classification of Algebra

Algebra may be divided roughly into the following categories:

• Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied. This is usually taught at school under the title algebra (or intermediate algebra and college algebra in subsequent years). University-level courses in group theory may also be called elementary algebra.
• Abstract algebra, sometimes also called modern algebra, in which algebraic structures such as groups, rings and fields areaxiomatically defined and investigated.
• Linear algebra, in which the specific properties of vector spaces are studied (including matrices);
• Universal algebra, in which properties common to all algebraic structures are studied.
• Algebraic number theory, in which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
• Algebraic geometry applies abstract algebra to the problems of geometry.
• Algebraic combinatorics, in which abstract algebraic methods are used to study combinatorial questions.

In some directions of advanced study, axiomatic algebraic systems such as groups, rings, fields, and algebras over a field are investigated in the presence of a geometric structure (a metric or a topology) which is compatible with the algebraic structure. The list includes a number of areas of functional analysis:

• Normed linear spaces
• Banach spaces
• Hilbert spaces
• Banach algebras
• Normed algebras
• Topological algebras
• Topological groups

The Significance of Calculus

While some of the ideas of calculus were developed earlier in Egypt, Greece, China, India, Iraq, Persia, and Japan, the modern use of calculus began in Europe, during the 17th century, when Isaac Newton and Gottfried Wilhelm Leibniz built on the work of earlier mathematicians to introduce its basic principles. The development of calculus was built on earlier concepts of instantaneous motion and area underneath curves.

Applications of differential calculus include computations involving velocity and acceleration, the slope of a curve, and optimization. Applications of integral calculus include computations involving area, volume, arc length, center of mass, work, and pressure. More advanced applications include power series and Fourier series.

Calculus is also used to gain a more precise understanding of the nature of space, time, and motion. For centuries, mathematicians and philosophers wrestled with paradoxes involving division by zero or sums of infinitely many numbers. These questions arise in the study ofmotion and area. The ancient Greek philosopher Zeno of Elea gave several famous examples of such paradoxes. Calculus provides tools, especially the limit and the infinite series, which resolve the paradoxes.

[News] - London student protests revisited

Students from all over the UK ( i.e. Scotland ) came to London today to protest.





Why?
- Fees are trebling from GBP 3,000 to GBP 9,000.
- The privatization of education will start.
- Entire faculties will be closed.
- And more.


Maybe the people behind these measures think that people will do anything to obtain a descent education including taking loans to finance university. From the USA we know that this means lifelong enslavement to the bank...


And that's just what they are protesting against at Occupy London ( and in zillions of other cities around the world ). So maybe the two will meet and join forces.


See also:
- [News] - London: More student protests

Graphica at Google Code

Graphica is now a real project. I don't know how many projects get started, I do know a lot of them die unfinished. I can only say that I hope this won't happen to Graphica. I will try to push it forward at a steady pace. It is not that I thought about it yesterday and well, started a project to 'see what happens'.

- I have been thinking about it for years.
- I silently programmed a prototype in Mathematica,
- made an extensive study of Mathematica graphics,
- studied how to develop a language-to-language compiler in Java,
- spec'ed the language,
- selected the Java frameworks, and tools to start with,
- chose a license

so: it's time to start hacking! At last. All I need now is a home for my code to live:

Graphica at Google Code.

Du Sautoy on CERN's speed of light result

I missed a Marcus du Sautoy ( pronounce: desoto ) documentary on CERN's issues on the speed of light. I watched it yesterday though. Another quality documentary by the BBC. I think there was a one-minute babble by the home expert on everything on Dutch tv. I have heard that the BBC receives hundreds if not thousands of complaints every week, well maybe that's what keeps them sharp.

To the point.

Faster than the speed of light could be made so fast due to the rich catalog of the BBC. A lot of material in this episode came from the catalog, no doubt. The struggles scientists had with light are explained up to the point that Einstein entered the scene and explained it all. Einstein said that the speed of light is the same everywhere and independent of how it is measured so time became variable which is hard to understand but true. Later Einstein said that time is the limit of speed in the universe. Nothing can travel faster than light. Voila $E=mc^2$.

Well, a neutrino traveled faster than light There are 16 types of fundamental particles, three of which are a neutrino. Pauli predicted neutrinos in 1930 but he thought it wouldn't be possible to ever find one. We are crossed by billions of neutrinos every second which is possible because everything, including us, is built up from atoms which are mostly empty. Neutrinos are extremely small and have no charge. But they still have a tiny mass so their speed is limited to the speed of light according to Einstein's laws. The amazing result from CERN is about neutrinos traveling faster than light.

For me, as a non-physicist, I find it unbelievable that it is possible to make such precise measurements. If the neutrinos and light were athletes running the 100m they would have beaten light only by a few millimeters.

Scientists are skeptical because time travel would become possible and it contradicts with previous results in the late 80s when it was measured that light and neutrinos emitted by a supernova reached us at almost the same time. But in favor of CERN is a previous result measured in Chicago which at the time was considered an error.

I lost it when Du Sautoy began about tachyons. Theoretical particles with imaginary or negative mass which could travel faster than light, mathematically of course, but so did anti-matter which was predicted through mathematics. There are also circumstances where an absolute speed limit doesn't make sense like black holes and the first second after the big-bang. And of course Einstein's theory and quantum-mechanics are incompatible.

String theory might have an explanation which satisfies everyone though. In their multi-dimensional bulk we live on a 3D membrane. It could be that the neutrinos left our membrane into the 4th dimension and so appeared faster. I bet a lot of SF fans could have come up with a similar explanation. String theorists are actually paid to talk about the fourth up to the 10th or eleventh dimension.

If you haven't seen the documentary yet, you'll be able to find it somewhere, I did.

Python Lesson 8

ഏറെ കുറ്റബോധത്തോടെയാണ് ഈ പോസ്റ്റ് നിങ്ങളിലേയ്ക്കെത്തിക്കുന്നത്. മാത്സ് ബ്ലോഗിന്റെ ഏറ്റവും വലിയ സംഭാവനകളിലൊന്നായി എടുത്തുകാട്ടാനുള്ള പേജ് 'പൈത്തണ്‍ പേജാ'ണെന്ന് നിസ്സംശയം പറയാം. ഗവേഷണത്തിരക്കുകളുടെ പാരമ്യത്തിലും മാത്​സ് ബ്ലോഗിനു വേണ്ടി പൈത്തണ്‍ പാഠങ്ങള്‍ ലളിതവും വിശദവുമായ രീതിയില്‍ തയ്യാറാക്കിത്തരുന്നുണ്ട് ഫിലിപ്പ് സാര്‍. എന്നാല്‍ (ഞാനടക്കമുള്ള) പലരും അതൊന്നും വേണ്ടത്ര പ്രയോജനപ്പെടുത്തുന്നതായി അനുഭവപ്പെടുന്നില്ല. മൂന്നോ നാലോ പാഠങ്ങളിലെവിടെയോ ഇടയ്ക്ക് വെച്ച് നിന്നുപോയീ പഠനം. ഏക ആശ്വാസം അതവിടെത്തന്നെയുണ്ടല്ലോ എന്നതാണ്. എന്നാല്‍ ഏഴുപാഠവും പഠിച്ച് എട്ടാമത്തേതിനായി കാത്തിരിക്കുന്ന ഭാമടീച്ചറെ പോലുള്ള പ്രോഗ്രാമിങ് കുതുകികളെ മറന്നുകൊണ്ടല്ലാ ഇതെഴുതുന്നത്. ഒരാഴ്ചയെങ്കിലുമായിക്കാണണം എട്ടാം പാഠം റെഡിയാണെന്നദ്ദേഹം അറിയിച്ചിട്ട്. അതെങ്ങനാ, കലോത്സവ,ശാസ്ത്രമേളാ സമ്പൂര്‍ണ്ണാദികളൊഴിഞ്ഞിട്ട് തലപൊക്കാന്‍ നേരം കിട്ടിയിട്ടു വേണ്ടേ..?ഇനി വൈകിക്കുന്നില്ല, ഇതാ എട്ടാം പാഠം.
Read More | തുടര്‍ന്ന് വായിക്കുക

Graphica preview

I don't think there are much limits, if any, to the graphics you can create with Mathematica, besides your own imagination of course.

My study project involves mathematics, computer science and art. It is called Graphica, it is basically an IDE to develop applications using Mathematica Graphics. For this I have designed a new simplified language to create -and animate- graphics. The most basic application is of course creating graphics. I have included some pics. Of course this is a project 'in progress'. I intend to release it as an open source app. More as the project develops.

The following images are candidates for the standard object library. They are created in Mathematica with SphericalPlot3D and are called 'butterfly' in Graphica.

Various polyhedra which are easy to create in Mathematica by accessing the PolyhedronData database functions.

More examples in one of my facebook albums, if you are interested.

Game Design: 6-10

Mark Rosewater, head designer for Magic: the Gathering, has up the 2nd part of his intro to game design article, so it must be time for my 2nd part of my commentary thinking about educational games.

The first five principles were:

1. Goal(s). Easiest part for educational games.
2. Rules.  
3. Interaction. 
4. Catch-Up. Most subtle, maybe because so many games lack this.
5. Inertia. Hard for teachers.

The second five:

6. Surprise. The game should have some unpredictability for players.

To me, this connects strongly to Interaction and Catch-Up. One way to get surprise is hidden information - which often can contribute to interaction amongst players.  Information can be hidden from both or the players can hide it from each other. The new game Flip Out has a good element of this with two sided cards of which each player sees different sides. A benefit for math and literacy is that this makes inference a part of the game.

The other easy way to add surprise is random events - which can contribute to making catch up possible.  The only thing that makes Monopoly playable is the dice rolling.  In Euchre, no matter how good you are, you need cards to play. The math benefit is the addition of probability, even if informal, to game play. It's no surprise that the two most common game pieces are dice and cards.

7. Strategy.

Interesting to me that this is so low on the list, which makes me wonder what he was ordering them to achieve.

by mhuang @ Flickr

This is the biggest add-on for educational games over other activities. The problem solving inherent in any game with strategy is such fantastic grist for mathematics.  Mathematicians often see math as a game because of this strong connection. How do we achieve a result with allowable moves? Using games with K-12 students,asking for their strategies always makes for an amazing summary and unearths most of the math content of the games. It also helps build Inertia as then students are more interested in playing again, trying our others' strategies or designing ways to beat them.

There's a natural tension between Surprise and Strategy.  If things are too random, strategy loses all impact. If things aren't random at all, it is chess or go.  Both great games, obviously, but also both games that struggle with Catch-Up and Inertia for many players. Plug for Magic: the balance of these two elements is a large part of what makes the game so bloody amazing. Also applies to Bridge, to a lesser extent. (Yes, I'm claiming Magic > Bridge.)

8. Fun.

I struggle with this. Because I find interaction, surprise and strategy so engaging, I love games in general. I'll play anything. But what makes a game fun to kids is often a surprise to me. It's not uncommon for me to take a game to kids, and let them add the context. I wrote about this a bit with my Division into Decimals game.  Games like Decimal Point Pickle and Power Up had this in spades. Probably this is the difference between a game being good, and the game being a smash hit.

To some extent I think the last two principles are really subcategories of this one. Did they get pulled out to make ten or - more likely - is there something I'm missing that makes them truly distinct?

9. Flavor.


10. Hook.

Flavor is about the context and setting for your game, which heavily influences the fun aspect for players, in my experience. At least on entry, and Mark connects this to the barrier or entry cost to your game. The other principles determine long term fun. In our house, this gets us to play a game fr the first time, but won't sustain interest. One neat point he makes about flavor, though, is how it can influence design. My youth Bible study is making a return of the Lord card game based on the 10 bridesmaids parable. (Yes, really.) But the context for the game is inspiring a four horseman of the apocalypse feature that will definitely add interest to the game. Probably shouldn't have shared this story.

The idea of constructive flavor reminds me of my colleague Jacqui Melinn talking about integrated units.  A marine biology integrated unit is not when you put your math practice problems on a whale-themed sheet, it's when your questions about whales require math to think about and solve. Good flavor isn't an add on, but supports the game mechanics. For a math game, this gets at the structure of the game supporting the mathematical objective. Cheap flavor is the hallmark of flashcard/drill math games. "Look you're doing lots of multiplication, but it's on a baseball diamond!"

Hook is what gets people to try your game. This is less important in educational games to me as we have a built-in market (students), but I'm also not trying to sell my games to a publisher. (So maybe my hook is that my games are free?)  However it does remind me of Dan Meyer talking about a hook for a lesson, and could well be linked to engagement. I just don't know how to tease it out from flavor and fun. Maybe hook is a measure of whether the game has things that make you wonder?

My Nine
Looking over the list, I think I'd order them more like the following to get at my process.

1. Goal(s). Design starts with objectives.
2. Structure. (Not in his list!) What is the essential nature of your set of learning objectives and how can that show up in the game?
3. Strategy. These three have to go into the primary design phase as well, or the game will just not have them.
4. Interaction.
5. Surprise.
6. Catch-Up. As you start to playtest, these two are important to attend to for good design.
   
7. Inertia.
8. Rules. For me this comes late; kind of a synthesis step as you think about how to communicate the game. It will often result in design revision, though.
9. Context: Fun-Flavor-Hook. To me this can't really be evaluated fully till you're out with the intended audience. You need a first take on this before that, but should be open to major changes in this area.

Boy, I enjoyed these two articles. Thanks, Mark, for  writing them, and giving us fledgling designers something to think about. Note that Mark has a Tumblr where he answers many questions and gives the behind the scenes story at Wizards of the Coast. I asked, for example, about the order of his list, and he wrote: "I left it up to my subconscious. That was the order that felt organically correct. I’ll be honest, that I can’t exactly explain why."

Images: All Magic: the Gathering stuff is very heavily (c)'d by Hasbro.

Tes Diagnostik Guru SMP

Tes Diagnostik Guru SMP untuk 4 mata pelajaran Ujian Nasional, Matematika, Bahasa Indonesia, Bahasa Ingris dan IPA akan diadakan pada tanggal 16 - 19 November 2011. Tes secara online ini dapat diakses di http://tesonline.simdik.info/

Berikut jadwal pelaksanaannya :

Download :

Surat edaran

Tata cara pelaksanaan

Latihan soal Tes Diagnostik Guru

Sumber : http://simdik.info/

Thoughts about number theory (1)

Has it ever happened to you that you skipped a proof because no matter how hard you tried you simply "didn't get it"? - Or worse, that you had to learn an algorithm but the 'why' wasn't given, let alone a proof. - Mathematics may be hard and difficult but at the end of the day you should 'own' the theorems. Where ownership stands for the notion that you could have created the theorem, in principle, yourself. Or look at ownership at this way: browse through a mathematics book that you studied two or three years ago, or even longer. Everything in it looks really simple because slowly over the years, you took ownership of that particular subject of mathematics.

When I am stalled on a particular topic or proof, I simply accept the proposition knowing that somehow my brain is working on it. It is a better alternative than remaining stalled. It is possible though that you are stalled because the author decided to leave out 'a few details'. Some topics in number theory, for example, are simple if you look at it from a group theory perspective. The author then has to decide if his proposed audience has already studied group theory or not. And even then his publisher may decide otherwise because from his perspective the audience should be made as large as possible.

Number Theory may be called the Queen of Mathematics the Queen needs a lot of help from the 'people'. There is analytical, algebraic, combinatorial and computational number theory and I wouldn't be surprised if there are a few more. The theory of prime numbers and group theory are strongly interconnected for example. Numbers are among the first mathematical objects that man studied but is a number an object? Unlike graphs, sets and geometric or topological shapes numbers don't really exist. Even groups exist, not just as sets, but they are part of nature itself in the form of symmetries everywhere. What -is- one? Like the one in 'one apple'? I argue that 'number' is a property like color, and the rest is just physics.

What about 'God invented the integers', 'Number theory is beautiful' and so on? The truth is that man invented a God that supposedly invented the integers. I have been studying number theory for a while now, and I haven't found its beauty yet. Just open problems, a lot of open problems everywhere. - Inspector Columbo would call that loose ends. And for him that is proof of human error. - That these open problems are a challenge is another issue.

Advice for Solving Equations

Quick post to share the teaching idea. The preservice high school teachers read 

“Advice for Solving Equations,” Steuben and Torbert, Mathematics Teacher, April 2006

The reflection was to give your advice. While I think the advice they give is solid, what I like is the giving of advice.

John G:
1) remember the meaning of the =. These things are the same thing, though they look different.
2) remember your purpose and for what you’re solving.
3) think about the best representation for solving this equation.

Ellen B:
1. Don’t forget about substitution! I wouldn’t have thought about this in the problem in the reading, but it made the problem so much easier.
2. Could you change the form of the equation to make it easier to solve?
3. Know what you’re solving for; what should the solution be in terms of?

Alyssa B:
1. Look at the problem before you start; what do you already know or what is important to note?
2. Make sure your answers make mathematical sense!
3. If you’re stuck, try rearranging/changing the form of the equation.

Greg O:
1. Never give up on a problem, if your stuck try rearranging it to make more sense to you.
2. Always look for things that you know in a problem so that you can maybe substitute something for it.
3. Make sure you can reverse the process so that you can get the original answer, a way of checking to make sure your answer is correct.

Jordan D:
1. It’s alright if you can’t get it right at first. You learn by spending time on the equation and from mistakes.
2. Experience helps you solve challenging equations, there are many steps that do not seem natural until we use them.
3.Always check your solution, make sure that it makes sense and works.

Emily W:
1. “You will get much more out of a problem if you work on it for 15 to 20 minutes and fail than if you turn to the solution after only 3 minutes.”
2. When you first start a problem, notice everything you can about the problem (Can x = 0? How many solutions will this equation give? Etc.).
3. If the method you are comfortable with does not come up with the correct solution, don’t be afraid to use one you are less comfortable with.

Mike Simon
1.) When solving a problem that looks difficult, begin by stating what you know.
2.) Work with what you know and if you get to a point where you are not sure if there is a next step, look over your work.
3.) After checking over your work, a make a guess and see where it leads you. There is not shame in being wrong.

Matt York
1. The whole purpose of the problem is defeated when you give the solution after just 3 minutes.
2.  As you are solving, always keep in mind the goal... never forget the purpose of the problem.
3. If you have no idea where to start, try some numbers which make sense in the context of the problem, it might lead you somewhere.

Joe Freiman
1. It’s better to work for 15 minutes and fail, than to look at the answer after a minute.
2. Using your past experience is the best way to solve difficult equations, so by practicing constantly and gaining more experience is the best way to get better at solving complex equations.
3. Check your work, make sure your answer makes sense.

EDIT: some end-of-the-semester catch-up-additions...

Brandi Stewart
1) It is ok to be wrong and have to try many different ways.
2) Check your work
3) It is not bad to ask for help, especially if you have tried the problem on your own and do not know how to figure it out.

Courtney Johnson
Mine are kind of specific but...
1) Try putting all variables on one side and setting equal to zero to see if using the quadratic formula is a possibilty
2) See if any substitutions can be made (e.g. trig identities)
3) Try removing a common factor to simplify

Amanda Hoezee
1) You will get much more out of a problem if you work on  it for15 to 20 minutes and fail than if you turn to the solution after only 3 minutes.
2) One does not need to be talented to solve challenging equations; one only needs experience.
 
Mitchell Brady
1) If you are stuck on a problem keep it simple and work with what you already know about the problem a solution that may help.
2) If you are stuck go back through your work to see if something sparks your memory to continue.
3) Finally, do not be afraid to continue and be wrong, just learn from your mistakes and try another method, but first figure out why it was wrong so you do not make the same mistake twice.

Ryan Warner
1) Failing isn’t always the worst thing, you can learn a lot sometimes by failing
2) There is almost always more than one way to solve a math problem, when solving equations this is definitely true so try different ways if you can’t figure it out right away.
3) Learn everything you can about the equation first before you try to solve it.

Shannon Penix
1) It is important to look at the problem all the way through before trying to solve it, noticing things you already know.
2) It is alright to take a while to get through a problem and even not succeed. At least there is learning involved.
3) Take the time to go back over your work if you get stuck. There may be earlier steps that could trigger your thinking to continue.

Jeremy Sheaffer
1) Be fair to both sides of the equation.
2) Check your work
3) The harder something is to learn, the more chance there is that you will remember it.

Image credit: dullhunk @ Flickr

കളര്‍ ഫോട്ടോകളെ ഒരുമിച്ച് ബ്ലാക്ക് ആന്റ് വൈറ്റാക്കുന്നതെങ്ങിനെ

ഒരു ചിത്രത്തിന്റെ നിറം എങ്ങിനെ ബ്ലാക്ക് ആന്റ് വൈറ്റാക്കി മാറ്റാം, എന്ന ആവലാതിയില്‍ നിന്നുമാണ് ഈ പോസ്റ്റിന്റെ ഉദ്ഭവം. ഒരു ഫോള്‍ഡറിലുള്ള കുറേയധികം ഫോട്ടോകള്‍ എങ്ങിനെ ബ്ലാക്ക് ആന്റ് വൈറ്റാക്കി മാറ്റാം എന്നറിയാന്‍ നമ്മുടെ ഹസൈനാര്‍ സാറിനെ വിളിച്ചപ്പോള്‍ അദ്ദേഹം അതിനൊരു മാര്‍ഗം പറഞ്ഞു തന്നു. സ്വതന്ത്രസോഫ്റ്റ്‌വെയറിന്റെ ലാളിത്യം നമ്മളിലേക്കെത്തിക്കാന്‍ മുന്നില്‍ നിന്നവരിലൊരാളായ അദ്ദേഹത്തെ അധ്യാപകര്‍ക്ക് പ്രത്യേകിച്ചൊരു പരിചയപ്പെടുത്തേണ്ട ആവശ്യമില്ല. ഇത്തവണയും ഒറ്റക്കമാന്റ് വിപ്ലവത്തിലൂടെ നമുക്ക് സഹായത്തിനെത്തിയിരിക്കുകയാണ് ഹസൈനാര്‍ സാര്‍. ഒരു ഫോള്‍ഡറിലെ ഫോട്ടോകളെ ഒറ്റയടിക്ക് ബ്ലാക്ക് ആന്റ് വൈറ്റാക്കാം. ബ്ലാക്ക് ആന്റ് വൈറ്റ് ആക്കുന്നതൊഴികെയുള്ള മറ്റുകാര്യങ്ങള്‍ മാനുവലായി ചെയ്യുന്നതാണ് ഉചിതം. എന്തുതന്നെയായാലും ഫോട്ടോയുടെ ക്ലാരിറ്റി ഉറപ്പുവരുത്തേണ്ടത് പ്രിന്റെടുത്ത് നോക്കി നമ്മള്‍ തന്നെയാണ്. വായിച്ചു നോക്കി അഭിപ്രായം പറയുമല്ലോ.

കളര്‍ ചിത്രങ്ങളെ ബ്ലാക്ക് ആന്റ് വൈറ്റ് ആക്കി മാറ്റാം.

1. ചിത്രങ്ങളുള്ള ഒറിജിനല്‍ ഫോള്‍ഡറിന്റെ കോപ്പി എടുത്ത് അതില്‍ Right Click ചെയ്ത് open in Terminal വഴി ടെര്‍മിനല്‍ തുറക്കുക.

mogrify -type Grayscale *.*

എന്ന കമാന്റ് കോപ്പി പേസ്റ്റ് ചെയ്ത് എന്റര്‍ ചെയ്യുക. ഇനി ചിത്രങ്ങള്‍ ബ്ലാക്ക് ആന്റ് വൈറ്റ് ആകുന്നത് ഫോള്‍ഡര്‍ തുറന്ന് നേരിട്ടു കണ്ട് ആസ്വദിക്കാം.

ഇത് നാം ഉദ്ദേശിച്ച രീതിയിലുള്ള അളവാണോയെന്നറിയാന്‍ പ്രിന്റെടുത്തു തന്നെ നോക്കണം. മുകളില്‍ നല്‍കിയിരിക്കുന്ന അളവുകള്‍ ഒരു ഉദാഹരണം മാത്രമാണ്.

NB: imagemagick എന്ന സോഫ്റ്റ്‌വെയറിന്റെ സഹായത്തോടെയാണ് ഈ കണ്‍വെര്‍ഷന്‍ നടന്നത്. ഇത് നമ്മുടെ സിസ്റ്റത്തിലുണ്ടോ എന്നറിയാന്‍ System-Administration-Synaptic Package Manager ലെ Quick Search ല്‍ imagemagick എന്നു നല്‍കി സെര്‍ച്ചു ചെയ്തു നോക്കുക. റിസല്‍ട്ടില്‍ ഈ പേരിനൊപ്പം പച്ച ചതുരം കാണുന്നുണ്ടെങ്കില്‍ ഈ സോഫ്റ്റ്‌വെയര്‍ നമ്മുടെ സിസ്റ്റത്തിലുണ്ട്. വെളുത്ത ചതുരമാണെങ്കില്‍ അതില്‍ റൈറ്റ് ക്ലിക്ക് ചെയ്ത് mark for installation നല്‍കി apply ചെയ്താല്‍ installation നടക്കും. തുടര്‍ന്ന് മുകളിലെ വിദ്യ പരീക്ഷിച്ചു നോക്കാം.
Imagemagick നെ കുറിച്ച് കൂടുതലറിയാന്‍ ഇവിടെ ക്ലിക്ക് ചെയ്യൂ

NB: ഒരുകാര്യം പ്രത്യേകമോര്‍ക്കുക. കുട്ടികളുടെ വളരെ പ്രധാനപ്പെട്ട ഡോക്യുമെന്റുകളിലേക്കായി നാം അപ്​ലോഡ് ചെയ്യേണ്ട ഫോട്ടോകള്‍ ഏറ്റവും ക്ലാരിറ്റിയുള്ളതായിരിക്കാന്‍ ശ്രദ്ധിക്കുക. കായികമേളയുടെ പോര്‍ട്ടലിലേക്ക് വേണ്ടി ഒരു ഫോള്‍ഡറിനുള്ളിലെ മുഴുവന്‍ ഇമേജുകളും ഒരുമിച്ച് format മാറ്റുകയോ resize ചെയ്യുകയോ ചെയ്യുന്നതിനായി converseen എന്ന സോഫ്റ്റ്​വെയര്‍ ഉപയോഗിച്ചതും ഉപകാരപ്പെടുത്താവുന്നതാണ്.

Google Public Data Explorer

Google Public Data Explorer is really a great tool of practice and exploration if you are doing a course in descriptive statistics. It is a sort of Google Maps - plus. Plus data. It does certain things that WolframAlpha does but interactive and with more data. You can even embed data that you created with this tool in your own webpages or reports.

The Google Public Data Explorer makes large datasets easy to explore, visualize and communicate. As the charts and maps animate over time, the changes in the world become easier to understand. You don't have to be a data expert to navigate between different views, make your own comparisons, and share your findings.

Try it yourself here: http://www.google.com/publicdata/home