Monthly Archives: February, 2013

The floor of the Duomo of Pisa

Floor of the Duomo of PisaPhotography by Carlos Dorce

Floor of the Duomo of Pisa
Photography by Carlos Dorce

Another interesting mathematical attraction which can be enjoyed in the Duomo of Pisa is the tiles of the floor. so if you go there you must look at the ceiling looking for the lamp and look at the floor looking for the tiles. Maybe you can find some other interesting attractions looking at the centre!

Location: map


Galileo Galilei’s lamp

The Duomo of PisaPhotography by Carlos Dorce

The Duomo of Pisa
Photography by Carlos Dorce

Another emblematic building of Pisa is the Duomo (the cathedral). Galileo Galilei was inside the cathedral when he observed the movement of the lamp hanging from the ceiling. He noticed that its oscillatory movement was constant so he discovered the isochronic property of the pendulum. The current lamp isn’t tha same lamp which Galileo observed that lucky day for the science (of course not!) but you can always look at it and try to imagine Galileo Galilei’s thoughts in that moment.

Photography by Carlos Dorce

Photography by Carlos Dorce

Look at it and enjoy this magic moment:

Galileo Galilei's lamp

Galileo Galilei’s lamp

Location: Piazza dei Miracoli (map)

The leaning Tower of Pisa

Tower of PisaPhotography by Carlos Dorce

Tower of Pisa
Photography by Carlos Dorce

Of course, if you travel to Pisa you’ll enjoy its famous leading tower. This emblematic monument of Pisa is the bell tower of the cathedral located in Piazza dei Miracoli. The construction pf the ground floor with a arcade with classical Corynthian columns began on August 14, 1173. After the third floor was built in 1178, the tower leaned due to its weak bases (only three meters deep!) and the unstable ground. Then, the construction was stopped. Giovanni di Simone restarted the construction in 1272 and the upper floors were built with one side taller than the other trying to compensate the inclination. Finally, the tower was finished in 1372 by Tommaso di Andrea Pisano.

Portrait of Vincenzo Viviani (c. 1690)
Domenico Tempesti (1652-1718)
Source: Wikimedia Commons

According to Vincenzo Viviani  (April 5, 1622 – September 22, 1703) who wrote one of the first biographies of Galileo Galilei, his master dropped two balls of different masses from the top of the tower in 1589. He wanted to demonstrate that their time of descent was independent of their mass. So he discovered that all the masses had the same acceleration when they fall down! So… Aristotle’s theory of gravity was absolutely false! Aristotle had said that all the objects fall at a proportional speed to their mass and Galilei’s experiment showed Aristotle’s mistake. Probably, Galileo Galilei didn’t do that experiment from the leaning tower and the legend written by Viviani is only a very good story but nowadays you can contemplate the leaning tower thinking that once Galileo Galilei was at its top refuting an Aristotle’s theory.

Location: Piazza dei Miracoli (map)

Another Galilei’s home

Vincenzo Galilei's homePhotography by Carlos Dorce

Vincenzo Galilei’s home
Photography by Carlos Dorce

Young Galileo Galilei spent his days around the current arcaded Piazza Vettovaglie running between the market shops. This part of Pisa is very interesting because you can see how Pisa was in the XVIth century and you can also imagine how those days in Galileo Galilei’s life were. Near this emblematic square there is the Borgo Stretto where you can find Vincenzo Galilei’s house in the days when Galileo was born:

Photography by Carlos Dorce

Photography by Carlos Dorce

This was another step in my scientific day in Pisa one week ago.

Location: map

Another 24-hour clock

Chiesa di San Giacomo di RialtoPhotography by Carlos Dorce

Chiesa di San Giacomo di Rialto
Photography by Carlos Dorce

Yesterday, while we were walking near Ponte di Rialto looking for a bar to drink a spritz, I found the Chiesa di San Giacomo di Rialto with a big 24-hour clock. Maybe I should look for some information about this kind of clocks:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: map

An astronomical clock in Venice

Astronomical clockPhotography by Carlos Dorce

Astronomical clock
Photography by Carlos Dorce

Today we’ve visited Venice. It’s not my first time in this city but today it has been snowing so it has been a special day. Piazza di San Marco is the central square of Venice and the place where the tourist find almost all the important buildings of the old city: the Palazzo Ducale, the Basilica di San Marco, the Biblioteca Nazionale Marciana,… Next to the Basilica, there is an interesting astronomical clock:

Photography by Carlos Dorce

Photography by Carlos Dorce

As you can see the Sun is located over Pisces (21st of February) and there is a typical 24 hour-clock around the astronomical clock.

What a wonderful day!

Location: map

The Verona Arena

The Arena of VeronaPhotography by Carlos Dorce

The Arena of Verona
Photography by Carlos Dorce

We have moved from Firenze to Venice and we have had lunch in Verona. Verona is very famous for being the stage of Shakespeare’s Romeo and Juliet as we can read in the prologue:

Two households, both alike in dignity,
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the fatal loins of these two foes
A pair of star-cross’d lovers take their life;
Whose misadventured piteous overthrows
Do with their death bury their parents’ strife.
The fearful passage of their death-mark’d love,
And the continuance of their parents’ rage,
Which, but their children’s end, nought could remove,
Is now the two hours’ traffic of our stage;
The which if you with patient ears attend,
What here shall miss, our toil shall strive to mend.

However, the main tourist attraction of he city is the Arena which is a Roman amphitheater built in the Ist century AD.  It was the forth biggest amphitheater of the Roman Empire due to its 30.000 “seats”. Mathematically, we can stand out the elliptical shape of its stage so we have again another mathematical reason to admire this Roman monument.

Source: Google Maps

Source: Google Maps

Location: Arena (map)

Roman figures in Ufizzi Gallery

Entrance to Ufizzi GalleryPhotography by Carlos Dorce

Entrance to Ufizzi Gallery
Photography by Carlos Dorce

Yesterday we arrived at Firenze and we visited the Museum Galileo Galilei of History of Science (which I will write some posts dedicated to) and today we have visited the wonderful Ufizzi Gallery. I think that I have some mathematical pictures taken today but now I’m so tired and I have chosen the one which seems easiest to explain: the main entrance to Vasari’s Corridor in Ufizzi Gallery. You can see in the photo the Roman Figures:


Notice that the Roman 1.000 is not exactly an M and Roman 500 is not exactly a D! In fact, the Roman 500 is originally the right half part of the Roman 1.000 and these figures had different forms before the known M and D. It has been a good opportunity to remember the Roman figures to some of my students!

Location: Ufizzi Gallery (map)

Nicolaus Copernicus’ doodle

Today is Nicolaus Copernicus’ 540th birthday and this is the doodle published by Google around the World. According to Doodle store:

An astronomer and mathematician, Nicolaus Copernicus is a shining star of the Renaissance. His major contribution to science is his heliocentric theory, which asserts that the sun is the center of our solar system. As the Earth was popularly assumed the center of the universe, his heliocentric theory rocked convention. Though the mechanics of this theory has mathematical underpinnings, its radical nature still gave Copernicus some pause. It was, therefore, not until his final year that he published his findings in De Revolutionibus orbium coelestium.
We wanted to celebrate Copernicus and his contributions to the world with a subtly animated doodle. Though revolutionary at the time, the heliocentric model is beautiful in its simplicity. The resulting doodle is zen-like and unassuming. Its actions need not scream for attention, much like the slow publication of De Revolutionibus orbium coelestium. The orbits of the solar system are steady and true

Galileo Galilei’s birthplace

Portrait of Galileo Galilei by Justus Sustermans (1636)
National Maritime Museum, Greenwich, London
Source: Wkimedia Commons

Today I begin a trip with my high school students for Northern Italy. Pisa, Firenze, Verona, Padova, Venice and Bologna are waiting for us and they are so excited with the idea of enjoying ​​art pieces, eating pizza and spending a wonderful week together in the magnificent Italian land. We left Barcelona yesterday at 20:30 and after a long journey traveling by bus, we have arrived to Pisa this morning. Pisa is a wonderful city and everybody wants to take photos to the famous leaning tower of the city. But… do you know that you can see Galileo Galilei’s birthplace walking by the narrow streets of Pisa?

Galileo Galilei was born in Pisa on February 15, 1564. Wikipedia summary says that:

Galileo Galilei was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism. Galileo has been called the “father of modern observational astronomy”, the “father of modern physics”, the “father of science”, and “the Father of Modern Science”.

His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), and the observation and analysis of sunspots. Galileo also worked in applied science and technology, inventing an improved military compass and other instruments.

Galileo’s championing of heliocentrism was controversial within his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism due to the absence of an observed stellar parallax.[9] The matter was investigated by the Roman Inquisition in 1615, and they concluded that it could be supported as only a possibility, not an established fact. Galileo later defended his views in Dialogue Concerning the Two Chief World Systems, which appeared to attack Pope Urban VIII and thus alienated him and the Jesuits, who had both supported Galileo up until this point. He was tried by the Inquisition, found “vehemently suspect of heresy”, forced to recant, and spent the rest of his life under house arrest. It was while Galileo was under house arrest that he wrote one of his finest works, Two New Sciences, in which he summarised the work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials.

Nowadays, Galilei’s first home is in Via Giuseppe Giusti and the house hosts a real-state agency:

Galilei's bithplacePhotography by Carlos Dorce

Galilei’s bithplace
Photography by Carlos Dorce

There is a little inscription that reminds to the visitor that this house is a very important building in the history of Science…

Photography by Carlos Dorce

Photography by Carlos Dorce

and there is also a little picture of Galileo Galilei in a corner of a window:

Photography by Carlos Dorce

Photography by Carlos Dorce

I am going to finish this post with another of the pictures that are going to be always in my mind:

Galileo's house and me

Galileo’s house and me

Location: Galileo Galilei’s birthplace (map)