I like to write about the different ways in which art and mathematics relate to each other. Today i bring to this space a new and motivating example. It is the interesting exhibition of the Brazilian artist Felipe Cohen, titled Broken Lights, that the gallery and publisher of art books Ivorypress has organized in its exhibition space in Madrid, from September 12 to November 3, 2018.

![1.jpg](https://cdn.steemitimages.com/DQmPXPhg19zfxt39StydJRmUgvn2PX4pD233prEy62ztW5e/1.jpg) *Work "Broken Lights Series # 51" (2017), acrylic paint on wood (24.6 ? 24.6 cm), by the Brazilian artist Felipe Cohen, inside the exhibition "Broken Lights" in the Ivorypress gallery in Madrid. Image of Ivorypress.*

This is an exhibition on horseback between painting and sculpture in which geometry and art dialogue with each other, and the artist Felipe Cohen makes the audience participate in that dialogue and the beauty that emanates from it. Using only right triangles, all of them with the same shape but of three different sizes, Felipe Cohen makes beautiful, suggestive and stunning portraits of nature landscapes. The Brazilian artist works with the triangular modules as if from a geometric puzzle, in the style of Tangram.

In the words of the author of the exhibition:

"My main objective was to portray nature as a field of constant indetermination and change, generated through systems. The construction of the geometry and the repetition of triangular modules provides control and rigor, while the appropriation of the organic nature of the wood grain and the watercolor process makes the natural marks of the material visible, creating an evocative, less graphic effect. "

https://cdn.steemitimages.com/DQmYDTZGxMYsL27MptWw3uymjdd3v4m6yA7s4uVyzPKgb3a/2.jpg) *Works "Broken Lights Series # 43", "Broken Lights Series # 51" and "Broken Lights Series # 45" (2017), acrylic paint on wood (24.6 x 24.6 cm), by the Brazilian artist Felipe Cohen, inside from the exhibition "Broken Lights" at the Ivorypress gallery in Madrid. Image of Ivorypress.* Ivorypress is an editorial specialized in art and artist's books that was founded in 1996 by Elena Ochoa Foster. Among the varied activities included in this project are the organization of art exhibitions, such as those organized in its art gallery in Madrid, the publication of different collections of art books and artist books, an educational program that aims to bring contemporary art to university education, audiovisual projects related to art and architecture, and the active library of the Madrid gallery specializing in photography, contemporary art and architecture. One of the hallmarks of Ivorypress is its exclusive artist's books. Among those he has published, we find artistic gems like Reflections (2002), by Eduardo Chillida, Open Secret (2004), by Anthony Caro, Wound (2005), by Anish Kapoor, The Secrets Life of Plants (2008), by Anselm Kiefer, Becoming (2009), by Ai Weiwei, or Tummelplatz (2017), by William Kentridge, among others. ![3.jpg](https://cdn.steemitimages.com/DQmX1vmugngADe7XBM3n2g9zDdViDUpdhgH4G2ChgtNDnJg/3.jpg) *Two photographs, one by Elena Ochoa Foster and the artist Isidoro Valcárcel Medina, in front of one of the volumes of the artist's book "Ilimit" (2012), by Isidoro Valcárcel Medina, and the other by the artist working on page 6 of "Ilimit " The edition consists of 9 volumes, plus two artist proofs, plus an H.C. (Hors Commerce stands for proof that it is out of trade). As explained on the Ivorypress page, "Ilimit" explores the contrast between the "limited" and "unlimited" concepts, while proposing a reflection on the concepts of seriation and exclusivity, so recurrent in the world of art. Each of the volumes is different and consists of 500 pages. The content of these pages consists solely of their numbering, correlative volume after volume from page 1 to 6,000. This pagination is written with ordinal numbering in different languages, chosen randomly from a total selection of 58 languages ??". Images of Ivorypress.* But let's go back to the current exhibition Broken Lights, by the Brazilian artist Felipe Cohen. This is the first solo exhibition in Spain of the artist born in Sao Paolo (Brazil) in 1976, and who received in 2016 the illy SustainArt prize at the ARCOmadrid fair. Among his individual exhibitions we find, among others, Ocidente at the Kubikgallery (Oporto, Portugal) in 2017 and at the Millan Gallery (São Paulo, Brazil) in 2016, Lapse at the Millan Gallery (São Paulo, Brazil) in 2013, Poente in Capela do Morumbi (São Paulo, Brazil) in 2013, Colagens in Anita Schwartz (Rio de Janeiro, Brazil) in 2009 or A Gravidade ea Graça in the Virgílio Gallery (São Paulo, Brazil) in 2008, as well as group exhibitions throughout the world. His works are in collections such as the Pinacoteca do Estado de São Paulo, Museu de Arte Moderna de São Paulo and Museu de Arte do Rio, Rio de Janeiro. ![4.jpg](https://cdn.steemitimages.com/DQmXcDgcDwau1TPyiPUbLHva5D2nCE9vNTyTmwS2V9ZCsbX/4.jpg) *"Untitled" (2004), by Felipe Cohen, glass and marble cup, 7 x 6 x 6 cm. Image of the Virgílio Gallery* Felipe Cohen uses all kinds of materials and means to develop his art. Make sculptures with found objects, collages with different materials, such as wood, paper or glass, installations, videos and drawings. ![5.jpg](https://cdn.steemitimages.com/DQmcU9LKAfew95hTTzw5eTFiKcTo3povJJPtVoENjcuBs7q/5.jpg) *“Catedral #2” (2010), de Felipe Cohen, pinza de la ropa de madera y travertino romano, 16,5 x 9,5 x 2 cm. Imagen de la Galería Estaçao* In the series of works Broken Lights, some of which are exhibited in the gallery Ivorypress (Madrid), the artist Felipe Cohen works one of the central themes of the history of art, such as the representation of landscapes of nature, but It does so in a very particular way, through a process of geometrization of the landscape that it wants to represent. To make these portraits, he uses a single geometric figure, a right triangle. These triangular pieces are made of wood, of three different sizes, but always the same shape, and, in addition, some of them are painted with a soft color (each piece a single color). By means of the combination of different triangles, the portrait of the corner of nature that one wishes to represent is created, for example, a beach, a lake, a valley or a cave. ![6.jpg](https://cdn.steemitimages.com/DQmSsXx9xVcEdJ4ehXHfcHEZHsZtcsrw6b46TrNTgy2s6YV/6.jpg) *View of the exhibition "Broken Lights", by Felipe Cohen, in the Ivorypress gallery, where you can see, from left to right, the works "Broken Lights Series # 30, # 29 and # 28" (2017), acrylic paint on wood. Image of Ivorypress.* The right triangle used by the Sao Paolo artist is always the same, its shape is not changed, although three different sizes are used. Let's see what triangle is this. To begin with, the triangle used by Felipe Cohen is a right triangle, then with a right angle, that is, 90º, which reminds us a lot of a square. Recall that the square is a drawing instrument whose shape is that of a scalene rectangle triangle, its sides are three of different lengths, whose angles are 30º, 60º and 90º. One of the properties of the triangle is that by placing two triangles together, stuck together by the longest leg, an equilateral triangle is formed, with the three sides equal, and the three angles also, of 60º. ![7.jpg](https://cdn.steemitimages.com/DQmV9SSX1ZAKFgfQkYo1w9roSKwazHRvybUr74hH8j9XQxe/7.jpg) *On the left, a right-angled scalene triangle of 30º, 60º and 90º angles, which gives rise to the shape of the square, and to the right an equilateral triangle, with the three equal sides, formed by the union of two triangles as the previous* But these are not the right triangles that Felipe Cohen uses. What shape do these triangles have then? As we can see in the works of the Broken Lights series with four right triangles, a square is formed (as can be seen, for example, in the upper part of the first frame, Broken Lights Series # 51), so the length of the cathetus greater than the right triangle is equal to twice the length of the short leg. In the following image we have drawn the shape of the triangles that Felipe Cohen uses, the big cathetus the double of the small cathetus, and we have also calculated, using the Pythagorean theorem, the length of the diagonal and, using a bit of trigonometry, the exact value of the angles of that triangle. ![8.jpg](https://cdn.steemitimages.com/DQmRzsYpkXXR8kGAJv9UBsc73GR36DAQ3cVwAAUQxjmvemW/8.jpg) *The geometry of the right triangle used by the artist Felipe Cohen in the series "Broken Lights"* ![9.jpg](https://cdn.steemitimages.com/DQmZNxW6fFVqxmcQTiNNkfj9d8PeGq77QwbiMwdGxFfwGwP/9.jpg) *Comparison of the shape of the right triangle of the bevel, on the left, and that used by Felipe Cohen, on the right* The work Broken Lights Series # 74, which would be the simplest composition of this series since all the works maintain the classic rectangular or square shape of a painting, is formed by two right triangles that form a rectangle of proportion 2, that is, the length is twice the width, in fact, the measurements of the work, without the frame, are 6 cm wide and 12 cm long. ![10.jpg](https://cdn.steemitimages.com/DQmcTEALzvR9QjevGfzVMaJWJYF7dAC7qziNrrBpJcBfBzH/10.jpg) *Work "Broken Lights Series # 74" (2018), acrylic painting on wood (6.5 x 12.5 cm), by the Brazilian artist Felipe Cohen, inside the exhibition "Broken Lights" in the Ivorypress gallery in Madrid. Image of Ivorypress.* And as I have said, with four triangles of those used by Felipe Cohen, a square can be formed, as shown in the following image. In addition, in this series of works three different sizes of right triangles are used. The three sizes used, given by the length of their legs, are 6 x 12 cm, 12 x 24 cm and 18 x 36 cm, respectively, so they can fit well triangles with others. In the work Broken Lights Series # 61 you can see the three sizes of triangles used. Next, we show the work and the structure of the triangles of it. ![12.jpg](https://cdn.steemitimages.com/DQmU6fjqJJnc3nTZeP9Nr6BQ5GeW5RtqfF12vaSU2Y5oRx1/12.jpg) *Work "Broken Lights Series # 61" (2017), acrylic paint on wood (36.4 x 36.5 cm), by the Brazilian artist Felipe Cohen, inside the exhibition "Broken Lights" at the Ivorypress gallery in Madrid. Image of Ivorypress.* ![13.jpg](https://cdn.steemitimages.com/DQmb3EvocCexCx3FqUokWQE6dBEwmc6WTkeHPzX66ZV2in7/13.jpg) Structure of the right triangles of the work "Broken Lights Series # 61", by Felipe Cohen. Another of the peculiarities of this series of works, which connects again with the history of art, is the use of color to give depth, three-dimensionality, to painting, which is a two-dimensional image. One of the works in which this effect is very well appreciated is Broken Lights Series # 73, which is shown below, which could perhaps represent the image of a cave, looking from the inside to the exit. Another element to highlight in this work is the use of spirals by contrasting color. ![14.jpg](https://cdn.steemitimages.com/DQmRp6MfTRoCebz3Nbsk6UJ5EZfS1CT886aY4SL6TEZUQQY/14.jpg) *Work "Broken Lights Series # 73" (2017), acrylic painting on wood (36.6 x 36.6 cm), by the Brazilian artist Felipe Cohen, inside the exhibition "Broken Lights" at the Ivorypress gallery in Madrid. Image of Ivorypress.* Although, the idea of using right triangles, in the manner of a geometric puzzle, such as the classic Tangram or other similar puzzles, has already been used by the artist from Sao Paulo in his work Chao ou Vao (2013), which includes from a series of 140 equal rectangles triangles of three colors (white, gray and black) that can be manipulated to build different landscapes on the rectangular case with transparent cover that acts as a painting, being therefore a dynamic work, never finished and always ready to be modified to create the next image. ![15.jpg](https://cdn.steemitimages.com/DQmbZKBPs2yTar4w9omMtQ24UeKHsGnJAiVMKZBqJmZKNNq/15.jpg) ![16.jpg](https://cdn.steemitimages.com/DQmd6uCntr2bdR4czacW4zgBHUYivv3G2Hz2H9vAbuUUNkm/16.jpg) ![17.jpg](https://cdn.steemitimages.com/DQmWw8oUqxKbNQN2mUENSatfRwjJWGM38sBw3nE8hb67FCg/17.jpg) *Three images of the work "Chao ou Vao" (2013), by the artist Felipe Cohen. Image of the Carbono Gallery* In the words of the artist: >"From wooden games such as the Tangram and others, which I saw frequently exposed in the workshop of the carpenter with whom I work, I began to think about the possibility of exploring the idea of ??non-definitive collages. From that central idea I developed the structure of that object / game using a geometric mesh formed by 140 mdf triangles of equal dimensions covered by Formica on both sides, but divided into three tones: one more luminous, close to white, and the other two in shades of gray, one lighter and one almost black. Enough to make it possible to draw drawings that suggest depth within that geometric mesh. The images found by me by the combination of these pieces are abyssal landscapes that suggest holes and hollows from the relationship of the lightest pieces with the dark ones. These pieces fit into a wooden case with an acrylic lid, which allows the assembly of this game on the wall, in a direct allusion to the frame ". To finish, simply recommend to people who can go through the Ivorypress gallery in Madrid to visit this magnificent exhibition and enjoy the geometric art of the Brazilian artist Felipe Cohen, and for those who can not visit it, to enter the website of Ivorypress and / or buy the Broken Lights catalog. #### Reference: 1. [Ivorypress, editorial and art gallery](http://www.ivorypress.com) 2. Felipe Cohen, Broken Light, Ivorypress, 2018. 3. Felipe Cohen, Trabalhos recentes, Galeria Marilia Razuk, 2012. ![mofeta.jpg](https://cdn.steemitimages.com/DQmUhncxq6tRGu1A5wiRPURXwY97KtyTWSMz1L77ocj5tPC/mofeta.jpg)