Shapes and Solids

8/7/2019 Shapes and Solids

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Ellsworth Kelly: Black/Yellow (1972)

What type of polygons can you see inthis painting?


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Ellsworth Kelly: Black/Yellow (1972)

I can see two triangles and a yellowquadrilateral called isosceles trapezium


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Frank Stella: "Ossipee from the Eccentric Polygons Series#99"1974

Do you Know the name of this polygon?


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Frank Stella: "Ossipee from the Eccentric Polygons Series#99"1974

This polygon is a REGULAR PENTAGON


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Frank Stella: litografas

And now, do you know their names?


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Frank Stella: litografas A SQUARE, AN HEXAGON, AN OCTOGON

AND A DECAGON


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Josef Albers

COULD YOU DESCRIBE THIS PAINTING?


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Josef Albers

I CAN SEE FOUR SQUARES PAINTED WITHDIFFERENT COLORS. The smallest square isyellow and the biggest is brown. The smallestsquares are inside the biggest square.


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James Turrell: Raemar

What type of quadrilateral is thisshape?


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James Turrell: Raemar

This shape is a QUADRILATERAL, but it is alsoa PARALLELOGRAM and a RECTANGLE too.


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Donald Judd: Untitled

And This shape?


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Donald Judd: Untitled

It is a RHOMBOID


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Ellsworth Kelly: Red Curve in Relief. (2009)

HELLO, MY NAME IS.


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Ellsworth Kelly: Red Curve in Relief. (2009)

HELLO, MY NAME IS:

RECTANGLE TRAPEZIUM (UK)


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Ellsworth Kelly: Lake I. (1982)

I am a very common quadrilateral, I havent

got any parallel sides.

May I introduce my quadrilateral family?


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QUADRILATERALS PARALLELOGRAMS

(Both pairs of opposite sides areparallel)

SQUARES

RECTANGLES

RHOMBUS

RHOMBOIDS

TRAPEZIUMS (Two parallel sides and two non-parallel)

OTHER QUADRILATERALS


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Alexander Rodchenko: Esfera de color y Crculo. 1918

Whats the difference between a

circle and a circumference?


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Alexander Rodchenko

Could you describe the relative position of circles and

straight lines in this painting?


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Alexander Rodchenko

We can see external and secant lines.

(The external line does not touch the circumference, the secant cuts the

circumference at two points).


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Duchamp: Rueda de Bicicleta. (1913)

Could you point outor enumerate some

elements of thecircumference?


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Duchamp: Rueda de Bicicleta. (1913)

Radius, Diameter,Chord, Centre,

Segment Circular.


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Alexander Rodchenko: Escalera

What type of straight lines are

these?


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Alexander Rodchenko: Escalera

They are PARALLEL lines


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Piet Mondrian: Composicin con amarillo, azul y rojo.(1942)

And these other lines?


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Piet Mondrian: Composicin con amarillo, azul y rojo.(1942)

PERPENDICULAR lines


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Theo Van Doesburg: Counter- Composition XVI indissonances. 1925

Doesburg and Mondrian were friends for years, but in 1924 they broke theirfriendship. The exact reason for this split has been a point of contention among

art historians; usually the divergent ideas about the directions of the lines in the

paintings have been named as the primary reason: Mondrian never

accepted diagonals, whereas Doesburg insisted on the diagonal's

dynamic aspects, and indeed featured it in his art.


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Ellsworth Kelly: Two Panels. (1968)

This is a TWO-DIMENSION painting, BUTwe have the impression we are watching a.................. Shape, that is a


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Ellsworth Kelly: Two Panels. (1968)

This is a TWO-DIMENSION painting, BUTwe have the impression we are watching aTHREE-DIMENSION Shape, that is a SOLID


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Tony Smith: Die. (1962)

Here we have a big POLYHEDRON,

Could you tell us its name and

describe it a little?


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Tony Smith: Die. (1962)

It is a Regular POLYHEDRON. Its name isCUBE. A cube is a polyhedron with six

faces that are perpendicular to one

another, and with all its edges equals.


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Sol Lewitt: Forms derived from a cube

Again, we are watching cubes, but this time both have

lost a corner. They are truncated polyhedra.

Could you named the missing polyhedra?


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Sol Lewitt: Forms derived from a cube

On the right-hand side cube there is a smaller cube

missing and on the left-hand side cube a pyramid.

Are you sure they are truncated polyhedra?


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James Turrell: Raethro Pink. (1968)

What type of Polyhedra are these works of art?

James Turrell


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James Turrell: Raethro Pink. (1968)

They are pyramids, square Pyramids.

The base is a square and the lateral sides are isosceles

triangles.

James Turrell


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Donald Judd: Untitle. (1989)

These polyhedra are called .There is also another solid in these pictures, canyou see it?

do you know its name?

Donald Judd: Untitled. (1963)


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Donald Judd: Untitle. (1989)

These polyhedra are calledCUBOIDS(0R QUADRANGULAR PRISM)

We can also see a Cylinder, and empty cylinder

Donald Judd: Untitled. (1963)


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Robert Morris: Seven plywood structures painted grey.(1964)

As you can see, this Morris work use

different kind of CUBOIDS


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Maurits Cornelis Escher: Reptiles

Could you describe this well-known painting byEscher from the mathematical point of view?


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Maurits Cornelis Escher: Reptiles

Escher uses three important mathematical ideas in this painting:Two-dimension world (a flat world)

Three-dimension world

Regular Polyhedra (Escher draws a dodecahedron)

Do you know anymore regular polyhedra?


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A regular polyhedron must meet two criteria:1) Its faces are identical regular polygons.

2) The same number of faces meet at each of the

polyhedrons vertices.


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Maurits Cornelis Escher:Hand with Reflecting Globe

Here you can see another kind of Solid: It is not a

Polyhedron because its form implies a curved surface.

Could you tell us its name?


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Maurits Cornelis Escher:Hand with Reflecting Globe

It is a SPHERE, OF COURSE


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Parmigianino: Self-Portrait in a Convex mirror (1523-24)

Parmigianino used the same technique asEscher to paint his self-portrait. His image

comes from a spherical mirror.


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Anish Kapoor:Untitle. Creation

We can say this solid is a ..


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Anish Kapoor:Untitle. Creation

We can say this solid is a hemisphere


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Anish Kapoor:Memory. (2008)

Imagine this big globe made of steel were the earth.

Could you tell us the name of the curved lines around

its surface?


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Anish Kapoor:Memory. (2008)

Parallels and Meridians. They are related to Latitude

and Longitude.


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Anthony McCall: Breath II. (2004)

Anthony McCall: Between You and I. (2009)

Are these light solids pyramids?


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Anthony McCall: Breath II. (2004)

Anthony McCall: Between You and I. (2009)

No, they are CONES, they bases

aren't polygons, but circles.


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Nancy Holt: Sun Tunnels. (1973-1976)

Look at this Land art work and tell us

the name of the solids you see


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Four CYLINDERS. A cylinder is a geometric solid boundedby two identical circles, called bases, and a curved lateral face.


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Now, look at the light

effects. Could you see twocircumferences with a common

tangent?


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Robert Smithson: Spiral - jetty . (1970)

As you can see, the name of this Land Art work is Spiral-jetty.

Here the author uses the SPIRAL form to express the

differences between human and nature activity.


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To Conclude: A piece of advice Dont

forget what you have seen


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LUIS M. RODRGUEZ MARTN

Mathematics DEPARTMENTIES ALBAYZNJANUARY 2011

Documents

Shapes and Solids