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INSTITUTE OF APPLIED MATHEMATICS (IMA) 
TRANSFORMATION OF A TWO-DIMENSIONAL SPACE 
TO A SPACE OF THREE 
By Emil Núñez Rojas 
3 
On 6 points drawn on paper 4 triangles can be drawn without 
repeating a line. These 6 points equals 6 edges of a tetrahedron 
and 4 vertices thereof in a three dimensional space 
. 
Over 12 points drawn on paper can be traced 8 square without 
repeating a line. These 12 points are equivalent to 12 edges of a 
cube and the 8 vertices of the same. 
About 30 points drawn on paper 20 pentagons can be drawn 
without repeating a line. These 30 points are equivalent to a 30
INSTITUTE OF APPLIED MATHEMATICS (IMA) 
edges and 20 vertices pentahedron it. 
On infinite points are infinite relations. This is equivalent to a 
sphere with infinite vertices. Within it can be drawn as a man of 
Vitruvius. Only within a sphere so man can rotate their limbs and 
has therefore has more freedom. 
Finally, the equation of the relationship between ratio of points on 
a plane and solid figures would be as follows: 
Where n = 1 is the ratio of a triangle (= 3lados), n = 2 the ratio of 
a square (sides = 4), n = 3 the ratio of a pentagon (= 5-sided), n = 
4 the ratio of a hexagon (= 6 sides), etc.
INSTITUTE OF APPLIED MATHEMATICS (IMA) 
The sequence of the solids in your order brings us to the 
relationship of the points with a solid sphere according to the 
formula. 
The formula and the theory contained in this paper is a discovery 
of Emil Núñez Rojas and are located in the School of Art Book: 
Methods to be original. Lima 2012. Perú. 
noverbal@hotmail.com 
face book: Emil Francisco Núñez Rojas 
cel: 954 638 125

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Transformation of a two dimensional space to a space of three discovered by emil núñez rojas

  • 1. INSTITUTE OF APPLIED MATHEMATICS (IMA) TRANSFORMATION OF A TWO-DIMENSIONAL SPACE TO A SPACE OF THREE By Emil Núñez Rojas 3 On 6 points drawn on paper 4 triangles can be drawn without repeating a line. These 6 points equals 6 edges of a tetrahedron and 4 vertices thereof in a three dimensional space . Over 12 points drawn on paper can be traced 8 square without repeating a line. These 12 points are equivalent to 12 edges of a cube and the 8 vertices of the same. About 30 points drawn on paper 20 pentagons can be drawn without repeating a line. These 30 points are equivalent to a 30
  • 2. INSTITUTE OF APPLIED MATHEMATICS (IMA) edges and 20 vertices pentahedron it. On infinite points are infinite relations. This is equivalent to a sphere with infinite vertices. Within it can be drawn as a man of Vitruvius. Only within a sphere so man can rotate their limbs and has therefore has more freedom. Finally, the equation of the relationship between ratio of points on a plane and solid figures would be as follows: Where n = 1 is the ratio of a triangle (= 3lados), n = 2 the ratio of a square (sides = 4), n = 3 the ratio of a pentagon (= 5-sided), n = 4 the ratio of a hexagon (= 6 sides), etc.
  • 3. INSTITUTE OF APPLIED MATHEMATICS (IMA) The sequence of the solids in your order brings us to the relationship of the points with a solid sphere according to the formula. The formula and the theory contained in this paper is a discovery of Emil Núñez Rojas and are located in the School of Art Book: Methods to be original. Lima 2012. Perú. noverbal@hotmail.com face book: Emil Francisco Núñez Rojas cel: 954 638 125