# 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

Church from BL Add 39636, ff. 5-8, 11-12, 30-32, f. 12. The British Library. Public Domain Mark

Kompozíció

Molnár Gabriella. Rippl-Rónai Megyei Hatókörű Városi Múzeum - Kaposvár

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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!

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?

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)!

And why is it so important to the world?

Let's watch this TED Ed movie!

Let's watch this TED Ed movie!

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 :)

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.

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!

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 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.

You can try to spirograph a rosette.

Can you?

**Inspirograph**

Can you?