Romanesque Math Discoveries
Mathematical discoveries in Romanesque Architecture: How the irrational Pi can be found in Romanesque Art and a cone can print a rosette
Cover Image from Europeana Collections
Church from BL Add 39636, ff. 5-8, 11-12, 30-32, f. 12. The British Library. Public Domain Mark
Romanesque Architecture
Romanesque architecture is an architectural style current in Europe from about the mid-11th century to the advent of Gothic architecture. It was a product of the great expansion of monasticism in the 10th–11th century.
Kompozíció
Molnár Gabriella. Rippl-Rónai Megyei Hatókörű Városi Múzeum - Kaposvár
CC BY
Kompozíció
Molnár Gabriella. Rippl-Rónai Megyei Hatókörű Városi Múzeum - Kaposvár
CC BY
Another example of Romanesque Architecture
The Route of the Romanesque
In Portugal there is an old and historical route... the Route of the Romanesque. On this route you will discover an ancient science, always so current and full of mysteries... mathematics…
Enter this fantastic, mysterious, mathematical world!
A hidden number and a fun story
In one of these places is hidden a number, also historical and of great importance. A number that's the main character in a fun tale. Shall we meet him?
UNESCO proclaimed March 14 as the International Day of Mathematics
Yeah, it's Pi! A number celebrated around the world on a mathematical day: March 14th is Pi Day (Pi is approximately equal to 3.14)!
The infinite life of... Pi
And why is it so important to the world?
Let's watch this TED Ed movie!
Let's watch this TED Ed movie!
Find Pi in Romanesque art
The number Pi is the quotient between the perimeter and the diameter of a circle.
And one of the most striking features of Romanesque art is precisely the use of semi-circular arches, where you can find number Pi!
Look for the Monastery of the Saviour of Paço de Sousa and discover a beautiful rose window (rosette), full of Pi!
Look for the Monastery of the Saviour of Paço de Sousa and discover a beautiful rose window (rosette), full of Pi!
Is that why it's so chubby :)
MathLapse Rosette
There’s a MathLapse that illustrates a process for constructing a stamp for imprinting a rosette which has (only) rotation symmetry.
And it’s this mathematics that we are going to study today: the relationship between Pi and the lateral surface area of a cone.
Math challenge - The rosette
Here's a good mathematical challenge:
The radius of the base of the cone, that stamps the rosette, corresponds to which part of the radius of the circle that constitutes the rosette?
First you have to know the formula to calculate the area of the lateral surface of the cone.
And then find the solution to our challenge.
Are you ready for a fun game? Let’s start!
Try a Math Composition!
And what about the rosette at the Monastery of the Saviour of Paço de Sousa?
Elaborate a mathematical composition where you explore the rosette of that Monastery and its rotation symmetry.
Suggestion: To obtain the relationship between the radius of the cone that prints the rosette and the radius of the circle that constitutes it you could have used the formula of the perimeter of the circle.
Shall we?
Don't forget to illustrate your ideas with geometric drawing.
Suggestion: To obtain the relationship between the radius of the cone that prints the rosette and the radius of the circle that constitutes it you could have used the formula of the perimeter of the circle.
Shall we?
Don't forget to illustrate your ideas with geometric drawing.
Spirograph - what is it?
Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
It was developed by British engineer Denys Fisher and first sold in 1965.
Inspirograph yourself!
You can try to spirograph a rosette.
Can you?
Inspirograph
Can you?
Inspirograph
