Wassily Kandinsky Wassily Kandinsky was born in Moscow in 1866. He grew up in a bourgois, cultured family and learned to play the piano and the cello. In 1886 he began to study law and economics at the Moscow University. After passing his exams he started a teaching career at the Moscow Faculty of Law. He had many interests and apparently a great gift to teach himself different skills. In 1895 Kandinsky saw an exhibition of French impressionists in Moscow with paintings of Monet and others. He was, at first, confused and would later describe how upset he was about Monet's painting The haystack. He thought that the painter had no right to paint things in a way that made it difficult to recognize the subject. In 1896, at the age of thirty, he decided to start a new career as an artist and went to Munich in Southern Germany. He enrolled at the Academy of Fine Arts for four years until 1900. Kandinsky became the theorist of abstract painting. In 1910 he created his first abstract work - a watercolor. In 1912 he published a book on the theory of abstraction. In 1922 he came back to Germany to teach and work at the Bauhaus in Dessau until 1933. When the German Nazis came to power in 1933, all modern art was considered as entartet (degenerated art) and the Bauhaus was closed in 1933. Kandinsky's works were removed from German museums and confiscated. The artist's next destination was Neuiily near Paris where he remained until his death in 1944.

Point Plane Ray • • Line Segment • Intersect Parallel Skew Lines A point is a location. It has no size. It is named with a capital letter. Line A line extends forever in both directions. Segment A line segment has two endpoints. The segment does not extend beyond those endpoints. • • Ray A ray has one endpoint and extends forever in the opposite direction. • Plane A flat surface that extends in all directions. It has no thickness Intersect If lines in a plane cross at a point, they intersect. Perpendicular If lines intersect at right angles, they are perpendicular. Parallel If lines in the same plane do not intersect no matter how far they are extended, they are parallel. Skew Lines Lie in different planes they do not intersect and are not parallel. A

Wassily Kandinsky's "Composition VIII" 1923; Oil on canvas; Solomon R Wassily Kandinsky's "Composition VIII" 1923; Oil on canvas; Solomon R. Guggenheim Museum, New York

An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. side The common endpoint is the vertex. side vertex

Wassily Kandinsky – “Composition IX”, 1939

Angles are measured in units called degrees. A protractor is a tool that measures angles Two angles are said to be complementary if they total 90°. Two angles are said to be supplementary if they total 180°.

Wassily Kandinsky: "Schwarzer Fleck", 1921

Adjacent angles share a vertex and a side but have no interior points in common. Vertical angles are formed by two intersecting lines and are opposite each other. Vertical angles have equal measure. Angles with equal measure are called congruent angles.

Black and Violet 1923

Triangle – A closed figure made from three line segments. Sides with the same length are congruent sides. Equilateral Triangle – A triangle with three sides of the same length. Isosceles Triangle – A triangle that has two congruent sides. Scalene Triangle – A triangle that has no congruent sides.

Yellow, Red, Blue 1925; Oil on canvas, 127x200cm; Centre Georges Pompidou, Paris

Acute Triangle – A triangle with three acute angles In order for three line segments to create a triangle, the sum of the two smaller segments must be greater than the larger segment. Acute Triangle – A triangle with three acute angles Right Triangle – A triangle with exactly one right angle Obtuse Triangle – A triangle with exactly one obtuse angle

Composition X 1939 (160 Kb); Oil on canvas, 130 x 195 cm (51 1/8 x 76 3/4 in); Kunstsammlung Nordrhein-Westfalen, Dusseldorf

Polygon – a closed figure made of line segments Regular polygon – a polygon in which all sides and all angles have the same measure Irregular polygon – a polygon with sides or angles that are not all congruent Quadrilateral – a four sided figure Pentagon – a five sided figure Hexagon – a six sided figure Octagon – an eight sided figure Decagon – a ten sided figure Regular Polygon Irregular Polygon

On White II 1923; Oil on canvas, 105 x 98cm; Centre Georges Pompidou, Paris

Trapezoid – a quadrilateral with exactly two sides parallel Parallelogram – a quadrilateral with opposite sides parallel and opposite sides the same length Rhombus – a parallelogram with all sides the same length, and opposite sides parallel Rectangle – a parallelogram with opposite sides the same length and all angles 90° Square – A square is both a rhombus and a rectangle. It has all sides the same length, and all angles 90°

Contrasting Sounds 1924; Oil on cardboard, 70x49 Contrasting Sounds 1924; Oil on cardboard, 70x49.5cm; Centre Georges Pompidou, Paris

 means “is congruent to” Congruent Polygons have the same size and shape. A figure that can be folded into congruent halves has line symmetry. A reflection is the mirror image of a figure that has been “flipped” over a line. An image and its reflection are always congruent..  means “is congruent to”

Wassily Kandinsky Title Unknown

Rotation – the image of a figure that has been turned, as if it were on a wheel Clockwise – when the top of a figure is turned to the right Counterclockwise – when the top of a figure is turned to the left Rotational symmetry – when a figure can be rotated less than full circle, and the rotation exactly matches the original image

Artist: Wassily Kandinsky Title: Farbstudie quadrate mit konzentrischen ringen Image Size: 20 x 30 in

Circle – Set of points in a plane that are all the same distance from a given point called the center, Radius – segment that connects the center of a circle to the circle. Diameter – segment that passes through the center of a circleand has both endpoints on the circle Central angle – angle with its vertex at the center of a circle. Chord – segment that has both endpoints on the circle. Arc – a part of a circle Semicircle – half of a circle

Circle Graph Circle Graph (pie chart) – a graph of data in which the circle represent the whole and each wedge is part of the whole. The total must equal 100%

Compass – A geometric tool used to construct a circle or part of a circle. Midpoint – point that divides a segment into two equal lengths. Segment bisector – a line, segment, or ray that goes through the midpoint of a segment. Perpendicular lines – lines that intersect to form right angles Perpendicular bisector – a segment bisector that is perpendicular to the segment.