Decomposition of the magic square on Drurer's Melancholia

Durer's Melancholia

Durer's Melancholia is world famous for its magic square on the top right wall.

16	3	2	13
5	10	11	8
9	6	7	12
4	15	14	1

It is a real magic square because it contains the integers 1,2, ..., 16 on 4x4 places. The constant of this magic square is 34. I have been thinking if there are any 'beautiful' ways in decomposing it into two or more (magical) squares. Best I have come up sofar are two squares with constant number 17.

1	3	1	12
3	10	0	4
9	1	6	1
4	3	10	0

15	0	1	1
2	0	11	4
0	5	1	11
0	12	4	1

Add them and the result is Drurer's magic square.

Memorizing digits of PI - revisited

A quality shared by all great mathematicians of the past is that they did not try to make an impression with their knowledge but instead shared their knowledge to the benefit of all. Someone who keeps his knowledge to himself demotes knowledge to a set of tricks and himself to a mere magician.

I don't know the author of the comment below but in the tradition of the best, he wrote the following comment to the post 'How to remember 1000 digits of Pi' which I received earlier this week but only read today. Not often do I receive a comment that I promote to a full post. As you will see it deserves to be.

Remembering the first 1,000 digits of Pi is a very simple task. It sounds daunting at first, but I assure you it is much easier than you think. The method you are using only complicates the process. You need to use the Dominic Method with the Journey Method. The Dominic Method uses 100 characters, each representing a number and letter code.

For instance: 11 on my list is Andre Agassi; his action is playing tennis, naturally. To remember 4 digits at one time, you pair 1 character with the 2nd characters action. So for the first 4 digits of Pi, we have: 3.1415 which corresponds to: Andy Dick writing on a blackboard (1415). AD=14, AE=15. AE is Albert Einstein and his action is writing on a blackboard. So pairing the first character and giving him the second character's action gives you a sequence of 4 digits.

The NEXT step, after memorizing your 100 person list (which gives you 10,000 memory storage locations) is to put them on a Journey. Take a familiar Journey around your house, neighborhood, etc. For instance, start in your bathroom: You have Andy Dick writing on a blackboard IN YOUR BATHTUB. Then you have Norman Bates (92) playing with toys (65)IN YOUR TOILET...then at your sink....you get the idea.

If you want clarification on this or help with your 100 person list, let me know. People have used this technique to memorize 75,000 digits of Pi. I have a journey with 1,000. A simple 50 mile round-trip stretch of highway with landmarks to "Put" these characters on will suffice for 250 storage locations of 4 digits (1 person with 2nd action) at each, which equals 1,000 digits. Email me at: 1fastbmw328@gmail.com if you want more info/help.

The author clearly knows what he is talking about as he refers to the Dominic method and the Journey method, both seem well known methods in the realm of memorizing. ( I must admit that I was not aware of either of them. Another reason why I enjoy learning new stuff. ) It seems that the key is Memorizing the 100 Person List. That is do-able, I suppose.

Clearly, I will start learning more about the methods and start experimenting with them. More soon.

#103 Hands on Math

Visit this blog and you will be amazed to see the teaching style!!

Hands On Math via kwout

Fast factoring using quantum computers.

“If somebody can build a quantum computer with all that it promises to be, prime number decryption could then occur in real time and that would mean all of the encryption that’s used by banks, governments and the military would be crackable.”
- Andrew Cleland, Ph.D., Physicist, UC-Santa Barbara"

Last Thursday, (31/3-'11) Linda Moulton Howe was on Coast with her monthly report. Linda covers environmental topics for Coast ( Japan quake, Gulf oil spill, mystery of the missing bee populations and so forth ), so I was surprised to hear her talking about prime number factorization.

All encryption nowadays is based on the RSA-encryption method which is a so called public-key cryptography method. The key required for enciphering is publicly known so that everyone can encipher data. Deciphering the data is only possible by the person who issued the key. The enciphering key is ( based upon ) the product of two very large primes while deciphering requires the individual primes. Cracking the code involves the factorization of a large prime number which we aren't very good at not even using brute force on networks of supercomputers. We simply can't do it.

Announcing that you are doing research that will eventually solve the prime factorization issue is of course mind-blowing. As I understood it they are going to build a machine that somehow mimics the quantum behavior of the particle world up-to a quantum computer. The analog of quantum mechanics is then that the computer computes everything until you ask it a question. So when you ask it to factor a large prime it comes immediately with an answer out of the scope of all answers. This answer is then immediately verifiable, something which we can do very fast.

Well, that's the idea. It won't work in all cases of course. Imagine the following question: Is the Riemann Hypothesis true? Yes (or No), will the quantum computer then answer. Remains the task for us to verify, and prove the RH.

This professor either does not understand the concept of Computability, or: he is very smart in using scare tactics to talk some money out of the pockets of some banks, or: his genius is multiple times greater than that of Alan Turing.

Coast to Coast is known for ( and owes its popularity to ) bringing the news 'unscreened' because 'it could be true'.

Geometry of a table

A mathematician is an organism that transforms coffee into theorems.
Paul Erdös

True. But I bet that he wasn't drinking his coffee at an ordinary coffee table.

പൈത്തണ്‍ പാഠങ്ങള്‍ തുടരുന്നു...

സെന്‍സസിലും എസ്.എസ്.എല്‍.സിയിലും ശമ്പള പരിഷ്കരണത്തിലും ഇലക്ഷനിലുമൊക്കെ കുടുങ്ങി പൈത്തണ്‍ ഏഴാം പാഠം പ്രസിദ്ധീകരണം നീണ്ടുപോയതിന് മാപ്പ്. ഏതാണ്ട് മാസമൊന്നായെന്നു തോന്നുന്നു, ഫിലിപ്പ് സാര്‍ ഈ പാഠം റെഡിയാക്കിത്തന്നിട്ട്. പ്രസിദ്ധീകരിക്കാന്‍ വൈകുന്ന ഓരോ ദിവസവും ചങ്കിടിപ്പേറുകയായിരുന്നു. "ഗവേഷ​ണത്തിരയ്ക്കുകള്‍ പോലും മാറ്റിവെച്ച് ഇത്രയും ഭംഗിയായി പാഠങ്ങള്‍ തളികയിലെന്നപോലെ തരുമ്പോള്‍ അതൊന്നു പബ്ളിഷ് ചെയ്യാന്‍ നിങ്ങള്‍ക്കെന്താ സമയമില്ലാത്തതെ"ന്ന വായനക്കാരുടെ ചോദ്യം എപ്പോഴാ പൊട്ടിവീഴുന്നതെന്നറിയില്ലല്ലോ..? 'വീട്ടില്‍ സ്വര്‍ണ്ണം വെച്ചിട്ടെന്തിന് നാട്ടില്‍ തേടി നടപ്പൂ..' എന്ന് ഒരു ടീമംഗം തന്നെ ചോദിക്കുന്നിടം വരെയെത്തി കാര്യങ്ങള്‍! അതെങ്ങിനാ, 'അലക്കൊഴിഞ്ഞിട്ട് കാശിക്ക് പോകാന്‍ നേരമില്ലെന്നു'പറഞ്ഞപോലായി കാര്യങ്ങള്‍. അതു പോട്ടെ.പാഠം 7 ഇതാ...
പൈത്തണ്‍ പാഠത്തിലേക്ക്...

Littlewood's advice to Ingham

My advice about studying mathematics is to go deep, to slowly let it sink in and revise, revise and revise. I.e. imagine a student who just reached the mandatory 360 (540) points: if he would not pass a subset of all his previous exams -today- wouldn't the degree be a joke? Anyway, I am all for a final exam covering a subset of all previous exams. - Yet, I don't think students will like the idea. But why not? Once the math is 'in' you would only have to maintain it during the lifetime of the course.

Hardy (l), Littlewood (r)

Ingham

An advice given by Littlewood to Ingham ( both were giants in Number Theory while Littlewood, together with Hardy of course, got Ramanujan to Cambridge ) is the following:

Albert Ingham was educated at Stafford Grammar School, and from there he won a scholarship to Trinity College, Cambridge, in December 1917. After spending a few months in the army towards the end of World War I, he began his studies in January 1919. An outstanding undergraduate career saw him awarded distinction in the Mathematical Tripos and win a Smith's prize and the highest honours. In 1922 he was elected to a fellowship at Trinity for a dissertation on the zeta function and his next four years were occupied only with research, a few months of which were spent at Göttingen. During this time Ingham was greatly influenced by Littlewood who gave him the advice to:-

... work at a hard problem: you may not solve it but you'll solve another one.

An advice I have taken long ago. When you generally work on harder problems than those presented to you in TMA's and/or exams, your TMA questions tend to become trivial. This is one possible method to score high marks for your TMA's. Other known proven recipe's which I do not advise are:
- ask someone with a degree 'to help you' ;
- target a student in the forums and offer him help ( not knowing he is going to do all the helping himself );
- post portions of your questions in Dr Math type of forums, mathematicians are very helpful;

If you have a blog ( in mathematics, or any other field ) and people start acting friendly then they are working towards asking you
- to 'exchange' some OU course books;
- to 'compare' answers on a TMA.
Make sure you always say NO, you don't owe them anything. Friendly visitors come in many disguises.

Siap Menghadapi Ujian Dan Ulangan Umum

......

Tak terasa sebentar lagi kita akan menjalani ujian dan ulangan umum. Nah, apakah kalian sudah siap untuk menghadapinya? Berikut ini terdapat beberapa tips yang dapat kalian lakukan untuk mempersiapkannya :

1. Siapkan waktu sebaik mungkin
Perhatikan urutan mata-mata pelajaran yang akan diuji lalu jadwalkan waktu untuk belajar. Mulailah untuk mempelajari mata pelajaran yang diujikan terlebih dahulu dari sekarang. Kurangilah waktu bermainmu. Jalankan kebiasaan ini setiap hari termasuk di akhir pekan.

2. Pelajari kembali catatanmu setiap hari.
Setelah pulang sekolah, biasakan untuk mempelajari kembali catatanmu. Hal ini dilakukan agar kita benar-benar mengerti pelajaran yang kita dapatkan di sekolah.

3. Lihat kembali tugas-tugas dan ulangan-ulanganmu yang sebelumnya.
Melihat kembali tugas-tugas dan ulangan-ulangan sebelumnya juga merupakan proses belajar. Coba lihat kembali dimana kalian melakukan kesalahan dan carilah jawaban yang benar. Siapa tahu apabila soal tersebut termasuk dalam soal yang diujikan, kalian sudah siap untuk menyelesaikannya dengan benar.

4. Buatlah kelompok belajar.
Dengan belajar berkelompok kalian dapat bertukar pikiran untuk membahas pelajaran yang kurang dimengerti atau sulit. Tetapi pastikan bahwa saat belajar bersama, kalian memang memakai waktu tersebut untuk belajar dan bukannya mengobrol.

5. Ikuti bimbingan belajar.
Salah satu pilihan yang dapat dilakukan untuk mempersiapkan diri kita menghadapi ujian atau ulangan umum adalah mengikuti bimbingan belajar. Dengan mengikuti bimbingan belajar, kita dapat memantapkan mata-mata pelajaran yang diajarkan di sekolah serta apabila kalian tidak mengerti, kalian dapat menanyakannya pada guru bimbingan belajar tersebut.

6. Jaga kesehatan tubuh.
Waktu ujian atau ulangan umum semakin dekat dan itu berarti kita harus belajar lebih giat hingga kadang lupa waktu. Karena terlalu lelah, kita jadi jatuh sakit, wah kalau begini kita jadi terhambat deh untuk proses belajarnya. Konsumsilah pula makanan yang bergizi yang mengandung 4 sehat 5 sempurna, jangan makan makanan yang sembarangan. Intinya, kita harus menjaga kesehatan tubuh agar kesehatan kita tetap prima sehingga akhirnya kita dapat menyelesaikan ujian atau ulangan umum dengan baik.

7. "Aku bisa!"
Kadang kita merasa tidak "PeDe" (Percaya Diri) akan menyelesaikan ujian atau ulangan umum dengan baik. Buanglah jauh-jauh pikiran itu dan katakan pada diri sendiri bahwa kita siap menghadapinya dan akan mendapatkan nilai baik. Dengan mempunyai rasa percaya diri, kita akhirnya dapat berkonsentrasi penuh dalam mengerjakan soal-soal yang diujikan.

8. Selesaikan belajar sehari sebelum ujian atau ulangan umum dimulai.
Biasanya kita sering tidak tidur dimalam ujian atau ulangan umum, sehingga akhirnya kita merasa mengantuk keesokan harinya, akibatnya kita tidak bisa menyelesaikan soal-soal ujian atau ulangan umum dengan baik. Agar hal ini tidak terjadi, usahakan untuk menyelesaikan belajar sehari sebelum ulangan umum dimulai. Lalu istirahatlah yang cukup agar tidak mengantuk disaat ujian atau ulangan umum.

9. Datanglah lebih pagi.
Akhirnya hari ujian atau ulangan umum tiba. Usahakan datang lebih pagi ke sekolah karena jika kalian datang terlambat yang akan kalian pikirkan adalah "semoga tidak terlambat." Karena merasa deg-degan, materi pelajaran yang kalian sudah pelajari jauh-jauh hari jadi terlupakan deh. Bayangkan kalau kalian datang lebih pagi kan bisa mengulang catatan.

Sumber : Dunia Belajar

Sites, Gadgets and Widgets

Warning: entirely a novice.  Trying to give that perspective on using these tools.

My university, Grand Valley State University, is in Michigan, a famously economically hard-pressed state.  Much like Wisconsin, any kind of education funding is suspect and under inspection.  We have think-tanks requesting faculty emails, and newspapers and TV stations soliciting financials.  (The financials are public info - no worries.  The emails - creepy.)

We got an email from the administration with some information to contest the spin being put on the data, and I started wondering about making it a webpage.  So I used it as a chance to practice with Google sites, embed a Google spreadsheet, and a Wolfram|Alpha widget.  Unfortunately, you can't embed a W|A widget directly, you have to wrap it in a Google gadget, then embed it in the site.  This site was very helpful, and the whole process boiled down to pasting the W|A javascript code in the Google gadget builder. I was using the builder at this page, just adapting their most basic example.

The W|A gadget was pretty easy to manufacture, following their steps.  After entering a request, you'll see options for sharing.  The far right W|A sigil starts the widget builder.

The thing that took me the longest to get was just me being dense.  To get at component properties, select a component in your proto-widget.  And then the settings will show in the bottom left.

Then to get the embed code to paste in your blog (will work directly) or to put in the gadget to put in a google site, click on the code button in the embed box on the finished widget.

The (sort of) finished project is here: Facts and More: How does GVSU stack up?

And, of course, I'd happily take any suggestions for improving that page. 

Petunjuk Teknis UN, US dan USBN 2011

Peraturan Gubernur Nomor 21 Tahun 2011 tentang Petunjuk Teknis Pelaksanaan Ujian Nasional, Ujian Sekolah/Madrasah, dan Ujian Sekolah Berstandar Nasional Mata Pelajaran Pendidikan Agama Islam Tahun Pelajaran 2010/2011

Untuk jadwal pelaksanaan UJian Nasional SMA/MA yang terdapat dalam lampiran IV Peraturan Gubernur Provinsi DKI Jakarta,

Tertulis :
Jadwal Pelaksanaan untuk Mata Pelajaran Kimia, Geografi, Sejarah Budaya/Antropologi, Hadist (jam kedua) pada UN Utama dan UN Susulan dilaksanakan pukul 08.00-10.00

Seharusnya :
dilaksanakan pada pukul 11.00 -13.00





Sumber : Disdik DKI

റെയില്‍വേയില്‍ പ്ലസ്ടൂക്കാര്‍ക്ക് സുവര്‍ണാവസരം

ഇന്‍ഡ്യന്‍ റെയില്‍വേയുടെ മെക്കാനിക്കല്‍ വിഭാഗത്തില്‍ സ്പെഷല്‍ ക്ലാസ് അപ്രന്റീസ് റിക്രൂട്ട്മെന്റിന് യൂണിയന്‍ പബ്ളിക് സര്‍വീസ് കമ്മീഷന്‍ അപേക്ഷകള്‍ ക്ഷണിച്ചു തുടങ്ങിയിരിക്കുന്നു. യോഗ്യതാ പരീക്ഷയില്‍ വിജയിക്കുന്നവര്‍ക്ക് ഇന്‍ഡ്യന്‍ റെയില്‍വേ സൗജന്യമായി മെക്കാനിക്കല്‍ ബി.ടെക് ബിരുദം നേടിക്കൊടുക്കുകുയും അതിനു ശേഷം ഇന്‍ഡ്യന്‍ റെയില്‍വേയുടെ മെക്കാനിക്കല്‍ വിഭാഗത്തില്‍ എന്‍ജിനീയറായി നിയമിക്കുകയും ചെയ്യുന്നു. ഈ പോസ്റ്റ്‌ നമുക്ക് വേണ്ടി അയച്ചു തന്നത് പാലക്കാട് മേഴ്​സി കോളേജിലെ (Mercy College) അവസാന വര്‍ഷ ബി.എസ്.സി കെമിസ്ട്രി വിദ്യാര്‍ഥിനി അനിത അരവിന്ദ് ആണ്. പരീക്ഷയെക്കുറിച്ചുള്ള വിവരങ്ങളും നോട്ടിഫിക്കേഷനും കഴിഞ്ഞ വര്‍ഷത്തെ പരീക്ഷാ ചോദ്യപേപ്പറുകളും ഇതോടൊപ്പം പി.ഡി.എഫ് രൂപത്തില്‍ നല്‍കിയിട്ടുണ്ട്. നോക്കുമല്ലോ.

സ്പെഷല്‍ ക്ലാസ് അപ്രന്റീസ് റിക്രൂട്ട്മെന്റ് പരീക്ഷ - 2011
വിദ്യാഭ്യാസ യോഗ്യത
പ്ലസ്ടു അഥവാ തത്തുല്യ പരീക്ഷയില്‍ കുറഞ്ഞത് സെക്കന്റ് ക്ലാസ് ആയെങ്കിലും വിജയിച്ചിരിക്കണം. അല്ലെങ്കില്‍ ബിരുദം ഉണ്ടായിരിക്കണം. മാത്തമാറ്റിക്സും ഫിസിക്സും കെമിസ്ട്രിയും പ്ലസ്ടു/ബിരുദത്തിന് പഠിച്ചിരിക്കണമെന്നും നിബന്ധനയുണ്ട്.
പ്രായം
2011 ആഗസ്റ്റ് 1 ന് 17-21. എസ്.സി/എസ്.ടിക്ക് അഞ്ചു വര്‍ഷവും ഒ.ബി.സിക്ക് മൂന്നു വര്‍ഷവും വികലാംഗര്‍ക്ക് പത്തു വര്‍ഷവും ഉയര്‍ന്ന പ്രായപരിധിയില്‍ ഇളവ് അനുവദിക്കും.
അപേക്ഷ എങ്ങിനെ അയക്കാം
www.upsconline.nic.in എന്ന വെബ്സൈറ്റില്‍ നിന്ന് അപേക്ഷ ഓണ്‍ലൈനായി അയക്കാം. ഓണ്‍ലൈന്‍ അപേക്ഷകര്‍ക്ക് 50 രൂപയാണ് ഫീസ്. അപേക്ഷ തപാല്‍വഴിയും അയക്കാവുന്നതാണ്. അപേക്ഷാഫോം എല്ലാ ജില്ലകളിലേയും ഹെഡ് പോസ്റ്റാഫീസുകളില്‍ ലഭിക്കും. അപേക്ഷകള്‍ക്ക് 100 രൂപയാണ് ഫീസ്. വനിതകള്‍/എസ്.സി/എസ്.ടി/വികലാംഗര്‍ എന്നിവര്‍ക്ക് ഫീസില്ല.
അപേക്ഷ സ്വീകരിക്കുന്ന അവസാന തീയതി
2011 ഏപ്രില്‍ 25
ഈ വര്‍ഷത്തെ പരീക്ഷാ തീയതി
2011 ജൂലായ് 31. കേരളത്തില്‍ കൊച്ചിയും തിരുവനന്തപുരവും പരീക്ഷാ കേന്ദ്രങ്ങളാണ്.
തപാല്‍ അപേക്ഷകര്‍ അപേക്ഷ അയക്കേണ്ട വിലാസം
Union Public Service Commission
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Dimensions - Documentary movie about mathematics

Dimension Two - Hipparchus shows us how to describe the position of any point on Earth with two numbers… and explains the stereographic projection: how to draw a map of the world.

Dimension Three – M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like.

The Fourth Dimension – Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension… and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces



Buy The DVD! If you like the movie.

M381 - TMA02 (1)

Looking ahead at M381 TMA02 Number Theory part.

TMA02 has 9 nine questions, 4 for Number Theory for a total of 50 points and 5 for Mathematical Logic also for a total of 50 points.

The Number Theory questions are about:
1. Chinese Remainder Theorem (10)
2. Congruences ( applied to ISBN numbers ) (11)
3. Fermat's Little Theorem (16)
4. Quadratic congruences / residues (13)

Doable, it seems (now).

More later on the ML part.

I noticed that TMAs 03 and 04 have been posted, so now the set is complete.

Paul Erdös - documentary

Some people consider Paul Erdös as the most prolific mathematician who ever lived. Born in Hungary in 1913, Erdös wrote and co-authored over 1,500 papers and pioneered several fields in theoretical mathematics. "N is a Number: A Portrait of Paul Erdös" is a documentary about his life and work. - It is now available for on line viewing on Internet. - N is a Number. Portrait of Paul Erdös.

Paul Erdös 1913 - 1996

Don't expect anything about his (other) addiction in this documentary. In an article by Paul Hoffman published in November 1987, Atlantic Monthly profiled Erdös and discussed his Benzedrine habit. Erdös liked the article, "...except for one thing...You shouldn't have mentioned the stuff about Benzedrine. It's not that you got it wrong. It's just that I don't want kids who are thinking about going into mathematics to think that they have to take drugs to succeed."

M381 TMA01 shipped

Just physically shipped M381 TMA01 to tutor.

This gives you a rough idea about the topics and available points per question. The qualifications 'easy, normal, hard and very hard' are of course my personal opinion.
1. Euclidean algorithm (12) - Normal
2. Mathematical induction (10) - Easy
3. Division (11) - Normal
4. Greatest common divisor (20) - Hard
5. Division (12) - Very hard
Number Theory (65)

6. URM trace and flow-chart (10) - Normal
7. URM programming (10) - Hard
8. Primitive recursion(5) - Hard
9. URM programming and primitive recursion (10) - Very hard
Mathematical Logic (35)

Counting very easy as -2 ( none this TMA ), easy as -1, normal as 0, hard as 1 and very hard as 2 yields a total which divided by the number of questions 9, added 10 and multiplied by 5 gives a hardness indicator ranging from 0 ( very easy ) to 100 ( very hard ). For M381 TMA01 (( 0 - 1 + 0 + 1 + 2 + 0 + 1 + 1 + 2 ) = 6 * 5 / 9 + 10 ) * 5 = 75.

So when I say that M381 TMA01 was hard you know exactly what I mean. ;-)

You may have noticed that the ratio ( Number Theory points / Mathematical Logic points ) is 2. This is because for this TMA we had to study 2 Number Theory OU booklets and 1 Mathematical Logic OU booklet. For TMA02 this is 2/2.