2019-06-21 (Midsommarafton)

Today, I learned that:

Today is the brightest day of the year on the Northern hemisphere, it is the day of the Summer solstice. You may remember that I already wrote about it briefly three years ago, on 2016-03-20, but here are some more interesting facts:

1. Summer solstice

The Summer solstice is the day of the year when one of the Earth’s hemispheres is located as close to the sun as possible. On the Northern hemisphere it happens around June 21 and on the Southern hemisphere around December 21. As a consequence, this is also the longest day of the year, considering the time from sun rise to sun set. But it also means that on the opposite hemisphere, it is the shortest day of the year. Read reference # 1 below for more information about the solstice.

So, which is the difference in duration of daylight in a particular place, if we compare those two dates? Well, the closer you live to the North Pole or the South Pole, the bigger the difference in time. You have probably heard about the expression “Midnight sun”, which is a phenomenon observed by those who live within the Arctic circle. As an example, in Kiruna, the northernmost city in Sweden, this year its habitants are lucky to have days with 24 h daylight from May 28 all through to July 16, a total of 50 days! But at the time around the December equinox, it is of course the opposite. From December 11, 2019 to January 1, 2020, during a total of 22 whole days, the Sun does not appear above the horizon not even a single minute!

And the closer one lives to the Equator, the less difference in time between the longest and the shortest day of the year. As an example, in Manaus, the capital of the Brazilian state of Amazônia, located 2 degrees South of the Equator, the difference is only 22 minutes, and in Macapá, the capital of the Brazilian state of Amapá, located exactly on the Equator, every day in 2019 is 12 h 7 min long. In my town Paranavaí, located slightly North of the tropic of the Capricorn, thus within the tropics, today is only 10 h 43 min long, whereas on December 21 it will be 13 h 34 min, a difference of 2 h 51 min. Reference #2 below has a link to a site that gives such information for any place on Earth, well worth studying.

2. UTC #1

And speaking about time, maybe you have noticed that the old abbreviation GMT (which stands for Greenwich Mean Time) is more often these days exchanged to UTC, how come?

I believe it is a matter of jealousy. Although the time settings for the globe are maintained within a zero meridian passing through the Greenwich observatory in UK, why should the British people have the privilege also to the name? So instead, UTC was introduced. Now, what does UTC stands for, exactly?

The fact is that it is a fabricated “abbreviation” involving English and French. Some centuries ago, the French had their own zero meridian for time, passing through Paris, but they had to succumb to Greenwich in that sense. So, as a compromise, they managed to enforce the denomination UTC. In English it would be similar to “Coordinated Universal Time” (CUT), and in French “Temps Universel Coordonné” (TUC), so UTC is not a bad compromise. Reference #3 has the whole story about it.

3. UTC #2

While I was doing research about UTC #1, I remembered that UTC is also the (real) abbreviation of a technical university in France, where I studied in the 1970s. I already wrote something about it on 2017-11-11, but here comes more. This UTC means Université de Technologie de Compiègne. It is a technical university belonging to the French state, created in 1972, and since 2012 it makes part of the group of Sorbonne Universities. It has a reputation of being more integrated into the society, with frequent trainee periods in the French industry, as well as many interchange programs with other international universities, than the traditional theoretical French technical universities, e.g. École Polytechnique.

I studied there between September, 1978 and June, 1979, exactly 40 years ago. During that year happened an interesting fact, a group of students from China came to study at our university. It was a sensation at that time, because China was extremely closed to external activities. This photo shows the Chinese students, taken in February, 1979. They have since kept the contact and met year after year and update themselves. See also reference # 4 below. At the bottom of that page you can also find the complete magazine edition of April 2019, both in French and English.

The group of Chinese pioneers who studied engineering at Université de Technologie de Compiègne, France. This picture was taken in February 1979, when they has just arrived at the university.

4. ISS flies over Paranavaí

The sensation today here in my home town was the passing of the international space station (ISS). I had heard about it before, that it would be possible to see it with a naked eye, but never had the chance to actually see it. It appeared today, and will reappear on the next Sunday June 23, when I will try to have a closer look and hope to take a better picture. See also reference #5 with the announcement.

This blimp is the international space station ISS passing over Paranavaí, PR, Brazil. Photo taken at 18:50 local time on 2019-06-21.

That’s what I learned in school !


1: Solstice

2: Kiruna, Sweden — Sunrise, Sunset, and Daylength, June 2019

3: Coordinated Universal Time

4: Des étudiants chinois à l’UTC depuis 40 ans

5: Estação Espacial poderá ser vista novamente no céu de Paranavaí

*: What did you learn in school today ?


2019-05-31 (Friday)

Today, I learned that:

I owe a big apology to all my faithful readers for having been absent with new posts for almost two months, so let me make it up today with a quite few interesting facts:

1. Image of a black hole

During the month of April, we received the astonishing news that astronomers had finally managed to catch a black hole on film. The image was captured by the Event Horizon telescope (EHT), a network of eight radio telescopes spanning locations from Antarctica to Spain and Chile, in an effort involving more than 200 scientists. Read more about it in ref. #1 below.

The image of a black hole captured by the Event Horizon Telescope. Photo by the EHT Collaboration team, consisting of 200 astronomers at eight different telescope sites.

2. Late Easter (continuation from earlier post)

In my post of 2019-03-05 I wrote about the late date of Easter this year, and as you may remember my friend, the German-Swedish meteorologist André Franke explained it all for us.

However, I have received comments about this subject. In 2019, the March equinox occurred on March 20, and there was a full moon already the next day, March 21. So, why was not Easter Sunday celebrated on March 24? André can explain that, as well. It is quite complicated, but here is the short explanation:

It all started in year 325, when the First Church Council of Nicaea among other things decided that the March equinox should always fall on March 21, and then Easter Sunday would always be the first Sunday following the first full month after the March equinox. But as we know, the Earth’s rotation around the Sun is not exactly 365 days. It is approximately 6 h more, and that causes that the fixed March equinox day is not always the same actual, astronomical day for the same equinox, as happened this year.

If you want know the long story, take a look at reference #2. Unfortunately, it is written in Swedish, but there are many other sources around the internet that can tell the same story.

3. Baarle

Baarle is a village right on the border between the Netherlands and Belgium. 91 % of the total area of the village belongs to the Dutch, the rest is Belgian. But it is not a clean cut, there are in fact 16 Belgian exclaves within the Dutch territory, and they in turn surround seven Dutch areas. See also reference #3 below. Thanks to Radio Sweden’s Andreas Liljeheden for yet another idea to an interesting blog fact, see also ref. 4 below! (You may remember Andreas’s earlier contribution to my blog on 2018-10-20, when he presented the donkey steps in the EU headquarters in Brussels.)

Andreas Liljeheden posing on a selfie in Baarle, in a street where both the Dutch and Belgian flags are blowing in the wind side by side.

4. Different maps of the world

One of my interests is maps, traditional, historic, different kinds of maps – you name them! It is therefore a great pleasure for me to present a total of 45 different maps of the world, the big majority of them are without doubt something you have never seen before. Click on the link of ref. #5 below and start being amazed. (I like maps #1, 2, 7, 8, …)

That’s what I learned in school !


1: Black hole picture captured for first time in space breakthrough

2: Vårdagjämning, fullmåne och ovanligt sen påsk: därför ser almanackan underlig ut 2019

3: Baarle

4: Andreas Liljeheden om ett avgörande EU-val

5: 45 Amazing World Maps

*: What did you learn in school today ?

2019-04-01 (April Fool’s Day!)

Today, I learned that:

Very recently, I received two pieces of sport news from Sweden which really made me both laugh and admire the initiative force of Swedish female athletes of all ages.

The first one is about curling. One week ago, Switzerland beat Sweden in the final of the women’s world championships, held in Silkeborg, Denmark, situated close to what was once considered to be highest point in Denmark. As you can see from this slogan, Danish mountain climbers have a blast there:

By the way, the highest peak here, called Himmelbjerget (which means the mountain of heaven) reaches impressive 147 m! See also reference #1 below.

But getting back to curling, one of the members of the Swedish team is called Agnes Knochenhauer. She won a gold medal in the Winter Olympics in PyeongChang in 2018, and after that, she and her team mates have won the European Championships and twice been runner up at the World Championships. In January this year, the same team from Sundbybergs CK also played in the Swedish Championships, held in Jönköping. Agnes let her 7-year old daughter, Tilda, visit the games together with her mother. Tilda has already started her own career and when the team skip, Anna Hasselborg, got sick, Tilda jumped in and replaced Anna, not as a skip, but as one of the other players. The result was beyond expectation, the team won the championships and little Tilda can now put Swedish adult champion on her business card! See also reference #2 below.

The Swedish champions 2019, from left to right: Anna Hasselborg, Agnes Knochenhauer, Tilda Knochenbahuer, Sara McManaus, and Sofia Mabergs. Photo taken on 2019-01-06 by Svenska Curlingförbundet.

And yesterday happened another interesting fact. During the last day of the Swedish Championships in biathlon, which had relay races on the program, another Olympic champion from PyeongChang, Hanna Öberg, also got sick and could not participate together with her teams mates in the women’s team event. That meant that her club, Piteå SSK, had to withdraw from the competition. But one of the two other team mates, Anna Magnusson, won a bronze medal nevertheless! She participated in the men’s (!) relay race with two male colleagues. See also reference #3 below.

The Swedish female biathlon athlete Anna Magnusson, now historic Swedish male champion, in a photo taken in Oberhof on 2018-01-04 by Christian Bier

That’s what I learned in school !


1: Silkeborg

2: 7-åriga Tilda ersatte OS-ettan och vann SM-guld

3: Anna Magnusson tog stafettmedalj – för herrar

*: What did you learn in school today ?

2019-03-05 (É carnaval!)

Today, I learned that:

As you probably have heard, one of the most important events during the year in Brazil is to commemorate carnival. For a complete description of what carnival is, I recommend that you consult reference #1 below.

The most important day during carnival is always on the final Tuesday, and this year it occurs very late, March 5. Normally it is in February, but from time to time it can be in March. I thought that March 5 would be the latest possible date for carnival Tuesday, but in order to be sure, I consulted an authority in the matter, a well known German-Swedish meteorologist named André Franke. If you live in Sweden, then you have probably seen and heard him on the weather forecasts. Here is what he told me:

Carnival Tuesday occurs 47 days before Easter Sunday and thus varies in the same way as Easter. This year Easter Sunday is April 21 and as consequence, Carnival Tuesday is on March 5. Next time this will happen is in year 2030.

However, the latest date that Easter Sunday can occur is on April 25, which will happen in year 2038. Carnival Tuesday will then be on March 9, 2038. Recently, in year 2011, it almost happened, Easter Sunday was on April 24 and Carnival Tuesday on March 8. All this is due to when the March Equinox occurs. Easter Sunday is the first Sunday after the first full moon on or after the March Equinox.

The Equinox, which is a point in time, can occur on different dates on different places of the Earth, due to the time zones, but Easter Sunday is on the same date all over the globe, and as a consequence also the Carnival Tuesday.

André also has his blog, see reference #2 below, where he details various astronomical facts occurring over the year. If that sounds interesting to you, then I definitely recommend that you look it up, it is well worth it!

The periodic table 150 years

Anyone who remembers their Chemistry lessons will surely also remember the periodic table. This table is an elegant composition of the different elements present in our universe. It was proposed by the Russian chemist Dmitri Mendeleev and first presented to the world on March 6, 1869.

Thanks to his way of organising the elements in a systematic manner, many new elements which only appeared as blanks in his original table were soon discovered and his forecasts about their properties were surprisingly exact. See also reference #3 below.

That’s what I learned in school !


1: Carnival

2: Astroinfo.se

3: Dmitri Mendeleev

*: What did you learn in school today ?

2019-02-28 (Thursday)

Today, I learned that:

The shortest month of the year is almost over and so is the period in Brazil when business is low. People want to enjoy Summer as much as possible, but once Carnival is over, there is no excuse any more. Roll up your sleeves and get started! In my next blog post, I will talk more about Carnival, why it happens in March this year etc.

Interesting mobile news

If you have followed my blog over the years, then you may remember that in 2016-06-07 and in 2016-06-19 I showed photos of what were then concept mobile phones, which could be expanded to bigger ones, with sizes typical to tablets, by simply unfolding them.

Well, comes 2019 and here they are! This month both Samsung and Huawei demonstrated their takes on this kind of phone. See pictures below and read about them in references # 1 and 2 below.

The two first hot versions of a foldable mobile phone. The two pictures on top show the Samsung Galaxy Fold and the two bottom pictures are of Huawei Mate X. Both are very pricey, US$ 1.980 and US$ 2.600, respectively, but let us hope that this concept is accepted by more makers so that it can be reality in every person’s pocket at a price they can pay!

That’s what I learned in school !


1: Samsung Unveils New $1,980 Galaxy Fold Smartphone

2: Huawei Unveils $2,600 Foldable ‘Mate X’ Smartphone to Rival Samsung’s Galaxy Fold

*: What did you learn in school today ?

2019-01-09 (3 years!!!)

Today, I learned that:

Time travels so fast! Exactly to the date, three years ago, I started this blog and it has been a fantastic experience. Thanks all you faithful followers for your support and advice. Unfortunately, during 2018 other commitments made me write very few blog posts, I will try to improve on that in 2019.

For all of you who have struggled with the puzzles I gave in the most recent blog, 2018-12-31, here are the solutions.

Which is the number of the parking space hidden by the car?

Look at the following image and you will see it immediately!

The busy fly

John von Neumann did not waste any time. After having replied immediately to the student who had posed the question, the impressed student asked the master if he had found the solution without making any calculations. No, on the contrary, I summed all the partial distances, was von Neumann’s reply.

But if you are no master in making calculations in your head, you can even beat von Neumann in speed by using the following reasoning: Any physics students knows that s = v x t, i.e. distance equals speed times time. Each cyclist travels 25 km using a speed of 25 km/h, so they will meet after exactly 1 h. The fly travels at 50 km/h during the same 1 h, i.e. a total distance of 50 km. QED!

That’s what I learned in school !


*: What did you learn in school today ?

2018-12-31 (Réveillon)

Today, I learned that:

There are so many beautiful natural scenes around us, if we only take the time to go looking for them. This month, I had the the joy of taking my family on a road trip to the southernmost states in Brazil, Santa Catarina and Rio Grande do Sul.

And it was really worth the while. Our main interest was to know the highlands in those states. In the latter one, we concentrated on “serra gaúcha” with the twin cities Canela and Gramado, and although they now are highly commercialised, they still offer quite some entertainment.

But the highlight of the whole trip was no doubt the highlands of Santa Catarina. In winter, many tourists go their to enjoy (?) snow in São Joaquim, but since that is something I have had way too much of in my life, I prefer the summer that has so much more to offer! Not far away from São Joaquim is one of the most breathtaking views in the world, namely the highway that serpentines Serra do Rio do Rastro down in 284 curves, from an altitude of 1 421 m to 220 m in a distance of a mere 12 km. Of course it is impossible to capture all the excitement in a photo, but I hope that today’s header photo, taken from the belvedere overlooking the abyss, can give you a hint. On a totally clear day, one can even see the Atlantic ocean, 100 km away!

See also references # 1 and 2 below.

Some things to think deeply about

I am sure that more than once in your life, you have been challenged to solve a mathematical puzzle that involves discovering the missing term in a sequence.

One such sequence is called an arithmetic sequence, where the difference between the consecutive terms is constant, e.g. 2, 5, 8, 11, 14, … Anyone promptly says 17 when asked of the upcoming term.

It gets a bit more complicated if I give you a geometric progression, such as 2, 6, 18, 54, … ; or 10, 5, 2,5 , 1,25, …; or even 1, 8, 27, 64, 125, …

But there is also a sequence of numbers that can really trick us, until we discover the underlying fact. Here is one of those, which is the number of the parking space hidden by the car in the following image?

Was that too easy? Try the next one then:

Two cyclists have decided to meet half way between their cities. The distance between the cities is 50 km. Both cycle at a constant speed of 25 km/h. At the very moment they begin their trips, a fly takes off from one of the cyclists and when it reaches the other one, it inverts its trajectory and flies back to the cyclist from where it started. When it arrives there, once more it inverts its trajectory and keeps on repeating the process until it has comes to a stop when the cyclists finally meet. If the fly holds a constant speed of 50 km/h, how far has it flown when the cyclists meet?

The brilliant mathematician John von Neumann, who proposed the computer architecture that now bears his name, was once asked the same question. One of his early skills was to make very complex calculations in his head, so he answered the question in a snap. Can you?

The solution will be published in my next blog post.

I wish you an EXCELLENT YEAR of 2019 !

That’s what I learned in school !


1: Serra do Rio do Rastro live

2: Serra do Rio do Rastro

*: What did you learn in school today ?

2018-11-11 (Guldsöndag)

Today, I learned that:

My prediction on 2018-04-15 was correct, 2018 would be the year of AIK. After the last round of Allsvenskan, the Swedish football championship league, once more AIK ended up being the very best! Oh how happy I am!

And as a tribute to the Stockholm region, where AIK has its headquarters, today’s photo shows a marvellous view of Stockholm. The photo was taken on 2018-11-04 from Skinnarviksberget, Södermalm and it shows the City Hall and Riddarholmen.

A photo of Stockholm, showing the City Hall and Riddarholmen, taken from Skinnarviksberget, Södermalm on 2018-11-04.

Furthermore, it is another photo in my series of hosts of the Olympic Games. Most people know that Stockholm was the host of the Summer Olympic Games in 1912, but did you know that it also hosted the Games in 1956? Since Australia had harsh quarantine restrictions, the equestrian events of the Melbourne games were moved to Stockholm. More about the Stockholm games can be found in references #1 and 2 below. Finally, today marks the exact centenary of the armistice after World War I. Exactly one year ago, I wrote about it extensively, you can find it here.

That’s what I learned in school !


1: 1912 Summer Olympics

2: Equestrian events at 1956 Summer Olympics

*: What did you learn in school today ?

2018-10-20 (Saturday)

Today, I learned that:

Continuing the post from 2018-09-29, here are two more interesting British facts from the world of Sports:

Wimbledon surrenders to John Isner

The American tennis player John Isner is, among other things, well known for having participated in the two longest fifth sets in the history of the Wimbledon tournament. In 2010, he beat the Frenchman Nicholas Mahut after winning the fifth set by 70-68, after three calendar days and 8 h 11 min of playing time. Then in this year’s tournament, in the semifinals, he lost to the South African player Kevin Anderson by 26-24 in the fifth set.

But that is the end of such marathon games, because as of 2019, Wimbledon has decided to introduce a tie-breaker at 12-12 in the fifth set.

See also references # 1 and 2 below.

Scotswoman breaks record for touring the world on a bicycle

In Britain, there are not only wonder women in golf. The Scottish cyclist Jenny Graham just arrived in Berlin after having gone on a tour around the world. You may remember that in the Jules Verne novel Around the World in Eighty days, her compatriot Phileas Fogg made it, using trains and steamer ships on 80 days. Jenny did not totally get there, but nevertheless her record is an amazing 124  days! (Another Brit, Mark Beaumont, holds the male record, set in September 2017, with 78 days 14 h 14 min., thus beating Phileas Fogg.)

Jenny Graham

Jenny Graham stops for a selfie while passing the Russian city of Pskov, close to the borders with Estonia and Latvia. Courtesy of Jenny Graham/The Adventure Syndicate/PA.

See also references # 3, 4, and 5 below.

Donkey steps

On various occasions, I have referenced material from Sveriges Radio (the Swedish Broadcasting Corporation), and here is yet another one:

Yesterday, their correspondent at the EU headquarters in Brussels, Belgium, Andreas Liljeheden, published a chronicle about the particular construction of the stair case between the two main buildings of the European Parliament. The following photo shows exactly that view.

EU steps

The court yard in the EU Parliament in Brussels, Belgium, highlighting the donkey steps between the two main buildings. Photo taken by Andreas Liljeheden on 2018-10-18.

As you can see, the vertical displacement from one step to another is small, but the horizontal one is much greater, exactly 1,16 m according to Andreas’ measurement. This makes walking up and down the stairs a complicated task. He investigated the origins of that crazy stair case, and found that in some countries of the European continent, such as Austria and Germany, there is a tradition of using deeper steps, whereas the Belgians and Dutch normally, due to the higher population density, have to settle with a different project, with a higher vertical-to-horizontal ratio. Sweden is, as always, “lagom”, i.e. mid-way.

Here are two more photos of donkey steps, the first one being a close-up of the EU Parliament steps, and the second one a typical scene of donkeys climbing the steps in Fira, the capital of the island of Santorini in the Greek Aegean Sea.


Two examples of donkey steps: To the left, a visitor to the EU Parliament in Brussels, Belgium (photo by Andreas Liljeheden, 2018-10-18). To the right, real donkeys in Fira, Santorini, Greece (photo by Liz Stark, 2016-04-06).

But why is Andreas emphasising this stair case? In no way, he implies that hard working politicians are donkeys, but he thinks it is a symbol for the difficulties encountered by the EU members. If you cannot have a unanimous decision on something by all its 28 member countries (soon to be 27?), then there has to be a compromise, such is life! Thanks Andreas for your valuable contribution!

See also reference #6 below.

That’s what I learned in school !


1: Longest tennis match records

2: Call It the John Isner Rule: Wimbledon Plans to Add a Final-Set Tiebreaker

3: Scottish cyclist smashes round-the world record

4: Around the World in Eighty Days

5: Around the world in 78 days: British cyclist completes record-breaking ride

6: Åsnetrappor typiskt för EU: Ekots Andreas Liljeheden, Bryssel

*: What did you learn in school today ?

2018-09-29 (When I’m 64)

Today, I learned that:

Once more, I woke up this morning with a tune in my head. And this time it was presented by the Beatles, and they dedicated it to me! Watch and listen to reference # 1 below.

Another extremely skilful Englishwoman is the amateur golf player Ali Gibbs. On 2018-08-17, she defended her club champion title at Croham Hurst Golf Club, South of London, with brilliance. In one of the 18-hole rounds, she hit two hole-in-ones, and in the other round yet another hole-in-one. (She had already scored three hole-in-one shots before in her career, on three earlier, distinct occasions).

Ali Gibbs

Ali Gibbs showing the three lucky balls. Photo by Simon Jacobs/Magnus News

The probability of an average golfer scoring a hole-in-one once in their life is calculated to be 1 : 12 500, for a professional to 1 : 2 500, but to hit three in only 36 holes is more than 1 : 1,9 trillion! Read more in reference # 2 below.

London, UK, River Thames

And while we are still in the London area, why not visit the capital. The photo above shows a beautiful bird’s eye view of River Thames and the Tower Bridge. London has already hosted the Olympic Summer Games on three occasions, in 1908, 1948, and 2012. More about those events can be found in references #3, #4, and #5 below.

That’s what I learned in school !


1: When I’m 64

2: 1.9 Trillion to one – Golfer Ali defies the odds to sink three holes-in-one in a day

3: 1908 Summer Olympics

4: 1948 Summer Olympics

5: 2012 Summer Olympics

*: What did you learn in school today ?