Tag Archives: Perspective

Snelson’s Neddle Towers

Needle Tower II (1969)
The Kröller-Müller Museum in Otterlo
Source: Wikimedia Commons

Kenneth Snelson (born June 29, 1927) is a contemporary sculptor who arranges rigid and flexible components to compose his sculptures combining tension and structural integrity. This Neddle Tower II (1969) is 30 meters high and it’s interesting here because of this picture:

Source: Wikimedia Commons

Is a mathematical picture or not? The sculpture is in the garden of the Kröller-Müller Museum in Otterlo.

LocationKröller-Müller Museum of Otterlo (map)

There is another Neddle Tower (1968) beside Hirshhorn Museum and Sculpture Garden on the National Mall in Washington, D.C.:

Source: Street View

Source: Street View

According to the Mathematical Tourist (by Ivars Peterson):

Snelson discovered the underlying principle for such structures in 1948, advocating the term “floating compression” to describe the balance between tension and compression and, in his sculptures, between flexible cables and rigid tubes. R. Buckminster Fuller (1895-1983) coined the word “tensegrity” (combining “tension” and “integrity”) for the same idea, and his term stuck. Snelson refers to weaving as the “mother of tensegrity.”

Snelson defines “tensegrity” as follows: “Tensegrity describes a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit.”
Snelson’s Needle Tower delivers a wonderful geometrical surprise when you venture underneath and look up to see a striking pattern of six-pointed stars.

This pattern arises naturally out of the requirement that each layer of a tensegrity structure consist of three compression elements (tubes). The sets of three alternate, giving the impression of a six-pointed star as you look up the tower. Snelson’s sculptures often show this kind of symmetry.

The elegance of Snelson’s tower suggests its use as an aesthetic alternative to conventional communications towers. But tensegrity structures are fairly elastic and flexible. They sway in the wind, which may not be ideal for the antennas and dishes that would top such structures.

Location: Hirshhorn Museum and Sculpture Garden (map)

Masaccio’s Holy Trinity

Masaccio’s Holy Trinity
Source: Wikimedia Commons

One of the most intersting frescos painted on the interior walls of Santa Maria Novella is the famous Holy Trinity by Masaccio (1401-1428). The fresco is too big (667 x 317 cm) and is located along the middle of the basilica’s left aisle. According to Wikipedia:

Although the configuration of this space has changed since the artwork was created, there are clear indications that the fresco was aligned very precisely in relationship with the sight-lines and perspective arrangement of the room at the time; particularly a former entrance-way facing the painting; in order to enhance the tromp l’oeil effect. There was also an altar, mounted as a shelf-ledge between the upper and lower sections of the fresco, further emphasizing the “reality” of the artiface.

This picture is very interesting for us due to the perspective which can be observed in it. Giorgio Vasari (1511-1574) wrote about it that:

a barrel vault represented in perspective, and divided into squares full of bosses, which diminish and are foreshortened so well that the wall seems to be hollowed out.

So Masaccio created a three-dimensional space behind the main stars of the picture. If we look carefully at the vault over God and Jesus we’ll be able to trace all the ortogonals in the ceiling and check that the vanishing point is located below the base of the cross. Masaccio designed this vaulted space in an empirical way althought the artistical illusion of depth isn’t so sophisticated.

Source: Wikimedia Commons

Anyway, when you come inside Santa Maria Novella, Masaccio’s fresco welcomes you and its vanishing point aligned with your eyes makes you feel a very good ad mathematical feeling:

Photography by Carlos Dorce

Photography by Carlos Dorce

Location: Santa Maria Novella (map)

Regular cubes?

Polyhedral monumentPhotography by Carlos Dorce

Polyhedral monument
Photography by Carlos Dorce

There is no doubt that this Eva Löfdahl’s monument is a set of a lot of crowed platonic cubes. I don’t know what this monument is dedicated to, but do you agree that it’s a mathematical attraction? When you are next to the monument you can see that there aren’t any cubes and everything is an optical illusion but… isn’t this perfect combination of diamonds a extraordinary geometric attraction?