Helmer ASLAKSEN

Picture Picture
More pictures Models of polyhedra made with Zome System
Home page of Edvard Jia-Xiong Aslaksen (艾加熊), born on February 13, 2006 Home page of Anna Jia-Xue Aslaksen (艾加雪), born on July 3, 2007

Professional Interests

Background and CV Research and List of Publications Teaching and Teaching Portfolio Directions to my Office and Home

Courses, Programs and Outreach Activities

Heavenly Mathematics & Cultural Astronomy Mathematics in Art and Architecture Special Programme in Science Joint ANU-NUS Master of Science in Science Communication
Public Lectures Student Projects Sudoku lectures and competitions in Singapore Singapore Mathematical Society
Why Calculus? Art Figures: Mathematics in Art. An Exhibition at the Singapore Art Museum Mathematics in Singapore Student Exchange between the National University of Singapore (NUS) and the University of Oslo (UiO)

Web Pages on Mathematics and Astronomy

Calendars in Singapore The Chinese Calendar The Islamic Calendar The Indian Calendar
When is Deepavali (Diwali)? Regional Varieties of the Indian Calendars Astronomical Java Applets, Animations and Video Clips The Mathematics and Astronomy of the Singapore Flag
What Does the Waxing or Waning Moon Look Like in Different Parts of the World? Why is Singapore in the “Wrong” Time Zone? Which Day Does the Sun Rise Earliest in Singapore? Where is the Geographical Origin of Coordinates of Singapore?
The Orbit of the Moon around the Sun is Convex! Why Are There Two High Tides Each Day? Myths about the Copernican Revolution A Guide to “The Sun in the Church” by J.L. Heilbron
“Fake” Armillary Spheres When Did the Millennium Start? Polyhedra The Ambassadors by Holbein
Niels Henrik Abel Proposal for a MAA Mathematical Study Tour "Norway: The Land of Abel and Lie" The Mathematics of Irish Elections My Reviews on Amazon.com

Web Pages on Computer Science

Reading and Writing Chinese Characters and Pinyin on the Web Using Unicode Chinese TeX Using the CJK LaTeX Package, Unicode TrueType Fonts and pdfTeX under Windows TeX Tricks HTML Tricks

Personal Interests

Blog Running Baking Color-blindness
Salsa Dancing in Singapore My Favorite Music English Subtitles for Flammen & Citronen Massage
Urban Legends My Pictures Family History Sound Greetings

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Professional Interests

Background and CV

My CV.

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Research and List of Publications

My list of publications.

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Teaching and Teaching Portfolio

My teaching portfolio.

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Directions to my Office and Home

I'm at S17 #06-20, 10 Lower Kent Ridge Road, Singapore 119076 Here are directions.

Here are pages about our home and old home. I'm trying to rent out my home for next year.

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Courses, Programs and Outreach Activities

Heavenly Mathematics & Cultural Astronomy

I've introduced a General Education Module called Heavenly Mathematics & Cultural Astronomy.

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Mathematics in Art and Architecture

I've introduced a General Education Module called Mathematics in Art and Architecture.

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Special Programme in Science

I am director of the Special Programme in Science. The Special Programme in Science was founded in 1996 as an an interdisciplinary programme for a select group of undergraduates with a deep passion for science. The students design a series of flexible and interactive multidisciplinary modules and plan semester-long research projects.

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Joint ANU-NUS Master of Science in Science Communicatione

I am director of the Joint ANU-NUS Master of Science in Science Communicatione. It is targeted at science and mathematics teachers and others who are interested in a career in science communication.

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Public Lectures

I give a lot of public lectures on mathematics, astronomy, art and education.

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Student Projects

I have supervised many exciting student projects.

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Sudoku lectures and competitions in Singapore

I have helped organized a number of Sudoku competitions in Singapore, both at the NUS and the Brand's Sudoku Challenge. I also give a lot of lectures on solving Sudoku. You can download a copy of the lecture notes.

Singapore Mathematical Society

I am vice-president of the Singapore Mathematical Society, and chairman of the organizing committee for the Singapore Mathematical Olympiad.

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Art Figures: Mathematics in Art. An Exhibition at the Singapore Art Museum.

I was mathematical consultant for the exhibition “Art Figures: Mathematics in Art” at the Singapore Art Museum.

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Why Calculus?

Together with Denny Leung I've introduced a course called “Why Calculus?” for the University Scholars Programme. It explains why calculus is important to mankind.

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Mathematics in Singapore

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Student Exchange between the National University of Singapore (NUS) and the University of Oslo (UiO)

I have created a page with information for students who go to go on exchange between the National University of Singapore and the University of Oslo. It includes a two complete course packages for mathematics students, but also information from students from other disciplines.

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Web Pages on Mathematics and Astronomy

Calendars in Singapore

One of my main interests is the Chinese, Islamic and Indian calendars. Have you always wondered how to compute the date of Chinese New Year, Eid ul-Fitr (Hari Raya Puasa) and Deepavali? I've written a paper on the Chinese calendar and a series of lecture notes, and I'm working on papers on the Islamic and Indian calendars. You will also see why both Eid ul-Fitrs (Hari Raya Puasas) in 2000 were celebrated one day earlier than they would have been if MUIS had relied on sightings or scientific criteria. You can find all this on my page on Calendars in Singapore.

I also have a separate page on When is Deepavali (Diwali)? and Regional Varieties of the Indian Calendars.

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Astronomical Java Applets, Animations and Video Clips

Together with Tey Meng Khoon and Frederick H. Willeboordse of CITA (Centre for Information Technology and Applications) I have developed interactive Java applets that I hope will help you understand the motion of the Earth, the Sun and the Moon.

Together with Keith Phua Kuan Wee of CITA I have recorded video clips to help you understand astronomical concepts.

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The Mathematics and Astronomy of the Singapore Flag

What is “wrong” with the Singapore flag? Why is the coat of arms more correct? I have a page on The Mathematics and Astronomy of the Singapore Flag.

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The Singapore Flag The Singapore Coat of Arms
The Singapore Flag The Singapore Coat of Arms

What Does the Waxing or Waning Moon Look Like in Different Parts of the World?

Together with Tey Meng Khoon and Frederick H. Willeboordse of CITA I have developed Java applets to explain What Does the Waxing or Waning Moon Look Like in Different Parts of the World?

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Why is Singapore in the “Wrong” Time Zone?

The short answer is that West Malaysia follows the time zone for East Malaysia, and that Singapore follows West Malaysia. For more details, please look at my web page Why is Singapore in the “Wrong” Time Zone?

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Which Day Does the Sun Rise Earliest in Singapore?

I have a web page on Which Day Does the Sun Rise Earliest in Singapore? Singapore lies almost on the equator, so most people would expect the Sun to rise at more or less the same time each day of the year. In fact, the sunrise time varies between 6:46 a.m. and 7:17 a.m., with the earliest sunrise on November 1 and the latest on February 9. In the same way, the sunset time varies between 6:50 p.m. and 7:21 p.m., with the earliest sunset on November 5 and the latest on February 13. The difference between the earliest and latest sunrise in 30 minutes, but the difference between the longest and shortest day is only 8 minutes. I'm working on a paper called The Analemma from a Tropical Point of View.

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Where is the Geographical Origin of Coordinates of Singapore?

Most capital cities have a geographical origin of coordinates, which is used when making maps for the country. All cities also have a zero point for road distances from the city center to other points. Why do capital cities need an origin of coordinates? In the past, finding coordinates, especially the longitude, was so hard that the best way was to pick a local origin, do astronomical observations at that point, and then do triangulation for the rest of the country. That's why the origin of coordinates is often at observatories.

In London the origin of coordinates is at Greenwich, while the zero point for road distances is at Trafalgar Square. In Oslo the origin of coordinates is at the Observatory, while the zero point for road distances is at Stortorvet. But what about Singapore? After a bit of detective work, and a lot of help from various people, I found that the origin of coordinates is at Empress Place and the zero point for road distances is at the old General Post Office, now the Fullerton Hotel. For more details, see my page on Where is the Geographical Origin of Coordinates of Singapore?

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The Orbit of the Moon around the Sun is Convex!

What does the orbit of the Moon around the Sun look like? Most people, even almost all mathematicians I've asked this question, tend to believe that it will have loops and look something like the picture below.

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In fact it looks like this picture!

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It is not a circle, but is close to a 12-gon with rounded corners. It is locally convex in the sense that it has no loops and the curvature never changes sign. (To be precise, it is more like a 13-gon, since we have to consider the sidereal month of 27.32 days instead of the synodic month of 29.54 days, and 365.25/27.32 = 13.37.) I have a page that explains why The Orbit of the Moon around the Sun is Convex!

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Why Are There Two High Tides Each Day?

Why are there two high tides each day? This is very frequently asked question! I used to think that the answer was simple, but after looking around in the library and on the web, I discovered several different attempts at explaining it. Newton's equilibrium theory from 1687 used the differential of the gravitational force, but some people (especially oceanographers) also consider a centrifugal force caused by the rotation of the Earth around the Earth-Moon barycenter. Unfortunately, it seems to me that the methods using a centrifugal force are unnecessarily complicated, if not outright wrong! I have a page on Why Are There Two High Tides Each Day?

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Myths about the Copernican Revolution

There are a lot of myths about the Copernican Revolution. Many people whose main interest is philosophy of science, but with little knowledge of astronomy or history of science, have written extensively about it. Unfortunately, much of what they say is incorrect. I have a page on Myths about the Copernican Revolution.

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A Guide to “The Sun in the Church” by J.L. Heilbron

The Sun in the Church: Cathedrals as Solar Observatories by J.L. Heilbron is an extremely interesting book. Unfortunately, it is not easy to read. It contains both serious mathematics and serious history. The purpose of the guide is to assist people who want to read it.

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“Fake” Armillary Spheres

I have come across two pictures of “Fake” Armillary Spheres.

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When Did the Millennium Start?

I have some contrarian views on when the Millennium started.

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Polyhedra

Together with my students I have made models of some interesting polyhedra.

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The Ambassadors by Holbein

I have a web page about this fascinating painting.

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Niels Henrik Abel

The Norwegian mathematician Niels Henrik Abel is my half third cousin fifth removed. Unless you are interested in genealogy, you probably don't even know what that means. And if you are interested in genealogy, you know that it's very easy to find link to other people like that!

Picture of Abel

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Proposal for a MAA Mathematical Study Tour "Norway: The Land of Abel and Lie"

The Mathematical Association of America's Mathematical Study Tour to Mexico in 2005 Zenith passage on May 25 at Chichen Itza (latitude 20.7N)

I had a wonderful time on the Mathematical Association of America's Mathematical Study Tour to Mexico in 2005. I feel that a Mathematical Study Tour of Norway would be a great idea and I proposed a tour to Norway in 2009 called Norway: The Land of Abel and Lie. After initially being accepted, it eventually got rejected, but I decided to keep this web page for sentimental reasons, and as a guide for other people who want to explore Norway on their own.

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The Mathematics of Irish Elections

Together with Gary McGuire, Department of Mathematics, National University of Ireland, Maynooth, I have written a paper on Mathematical Aspects of Irish Elections. The paper discusses the rules for the Irish elections. In particular, it discusses the problems with only considering the last sub-parcel received.

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My Reviews on Amazon.com

I've written a number of reviews on Amazon.com about books on mathematics and astronomy. If you find my reviews helpful, don't forget to vote for them! :-)

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Web Pages on Computer Science

Reading and Writing Chinese Characters and Pinyin on the Web Using Unicode

I studied English, French and German in school in Norway, and Chinese for two years at Berkeley. Unfortunately, my pronunciation sucks in all languages!

Because of my web page on the Chinese calendar, I need to put Chinese characters and pinyin on the web. You may want to look at my page on Reading and Writing Chinese Characters and Pinyin on the Web Using Unicode.

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Chinese TeX Using the CJK LaTeX Package, Unicode TrueType Fonts and pdfTeX under Windows

The CJK LaTeX package by Werner Lemberg is a wonderful tool, but it can be a bit hard to install if you're not using Linux. Fortunately, it is now part of both TeXLive and MiKTeX. However, using Unicode TrueType fonts and pdfTeX involves some additional steps, so I wanted to share my solution with other people.

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TeX Tricks

I have written a paper called Ten TeX tricks for the mathematician, TUGboat, Communications of the TeX Users Group 14 (1993), 135-136. I have also collected various other TeX tricks that I wish somebody had put up on the web when I was struggling to figure it out for myself!

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HTML Tricks

Here are some simple HTML tricks that I have put up mostly for my own reference.

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Personal Interests

Blog

I have a blog called Aslaksen-Singapore, where I put up pictures of the kids and my baking.

Running

My personal best are 3,000: 8.42, 5,000: 14.55, 10,000: 31.01, marathon: 2.39.59. I also ran the 3,000 steeple chase once in about 9.30. My best race was in 1982 when I placed 19th in the Northern California Cross-Country Championship in San Francisco. In Singapore I've won the SAAA Cross Country Championship and placed second in the Mobil Marathon. In Singapore I run for MacRitchie Runners 25, in Norway I run for OSI (University of Oslo Students Sports Club) and in the San Francisco Bay Area I run for Pacific Striders.

On Thursdays we run hills in Kent Ridge Park. Please look at the map for directions. Jukka and I meet at the intersection of Prince George's Park and Kent Ridge Road at 6:25, or you can meet us by the pond in Kent Ridge Park at 6:30 p.m. Please look at the map for directions.

On Tuesdays we run threshold runs at Bukit Brown Cemetery. We meet at the track at NUS Bukit Timah at 6:15 p.m. or at the Cemetery at 6:30. For more details, please consult our Yahoo Group.

Picture of the OSI (University of Oslo Students Sports Club) centipede. Centipedes were first introduced in the 1978 Bay to Breakers race.

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Baking

My grandmother was an excellent baker, and baking brings back fond memories of her. My children never met her, but I want her to live on in my cakes, cookies and breads. Another reason why I love baking is that while cooking is an art, baking is a science! To me baking is a wonderful combination of family, culture and science. I have put some recipes up on my baking page.

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Color-blindness

About 8% of men are color-blind, but only about 0.5% of women. Thanks to the examples page from Vischeck's color-blindness simulator you can now see what the world looks like to us!

There are four main types of color-blindness.

I'm protanomaly or red-weak. If you are color-blind, but don't know what type, you can look at some of these tests.

If you are color-blind and want to get a sense of what a picture looks like to people with normal color vision, you can try Daltonize from Vischeck.

Here are some sites with general information.

Some people claim that in certain situations color-blind people are at an advantage.

If you are color-blind and having problem viewing graphics on-line, you may want to check out eyePilot software from colorhelper.com.

Another interesting question is how different languages describe colors. A good starting point is the Wikipedia page on Distinguishing blue from green in language.

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Salsa Dancing in Singapore

Salsa Rueda with Fen, Junice and Nick at
the JitterBugs Xmas party 2000
Salsa Rueda with Fen, Junice and Nick at the JitterBugs Xmas party 2000

I love to dance Salsa! My Salsa page gives information about Salsa classes, Salsa videos, Salsa steps and Salsa music.

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My Favorite Music

I have a very diverse taste in music, but my primary interests are world music, especially Celtic, Scandinavian and Latin, and punk rock. Please check out my music page.

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English Subtitles for Flammen & Citronen

There are a lot of excellent movies made in Scandinavia these days, but unfortunately, some of them are released without English subtitles. Here are some English subtitles I wrote for Flammen & Citronen.

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Massage

I'm a licensed massage therapist. I did my training at Mueller College of Holistic Studies in San Diego, California.

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Urban Legends

There's a lot of chain mail about urban legends circulating by e-mail. The best sites for learning the truth about these stories are Urban Legends and Folklore at about.com, The AFU & Urban Legends Archive and Urban Legends Reference Pages.

One common e-mail chain letter is the one that seems to magically determine your age, just based on you telling them how many times a week you like to eat pizza, eat chocolate or something like that. I don't want to be spoil-sport, but I don't understand why people are so amazed by this one. If I tell you my year of birth and whether I've had my birthday or not this year, then you don't need a Ph.D. in mathematics to figure out my age! I've written a page to explain this.

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My Pictures

Here are some more pictures.

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Family History

My family history (ahnentafel). This file is long!

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Sound Greetings

Do you want to know how to pronounce my name? I have made a recording of my name in Norwegian. There is no “correct” way to pronounce my name in English, and in fact, I often change the way I pronounce my name in English, but here I have recorded one possible way to pronounce my name in English. I have also recorded short greetings in English and Norwegian.

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Good-bye!

Congratulations! You've made it to the end of my home page! Thanks for your patience! I hope you have found something of interest. That makes my efforts worthwhile. Feel free to send me a message. Have a nice day!

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Helmer Aslaksen
Department of Mathematics
National University of Singapore
helmer.aslaksen@gmail.com

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