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A GEOMETRIC APPROACH TO DEFINING MULTIPLICATION

A GEOMETRIC APPROACH TO DEFINING MULTIPLICATION 2025

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The document presents a geometric approach to defining multiplication, arguing that current mathematics education lacks rigorous definitions and proofs related to multiplication, area, and similar triangles. The authors propose that these concepts should be defined independently in the curriculum. They introduce a geometric definition of multiplication using parallel lines and demonstrate how this definition can be used to prove various properties of multiplication, including its relationship with areas of triangles and the concept of similar triangles. The paper aims to enhance understanding for prospective K-12 math teachers and STEM students by providing a clear visual interpretation of multiplication.

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What is the geometric approach?

The Geometric Approach. The geometric approach is so called because in it the quadric surfaces are instead represented by points, vectors, and scalars that are specific to each type of surface. For example, spheres are represented by a centerpoint and radius.

Is there multiplication in geometry?

14:11 29:23 Again the fact that multiplication is commutative. Allows you to do this in two steps. Either rotateMoreAgain the fact that multiplication is commutative. Allows you to do this in two steps. Either rotate first and then stretch. Or stretch first and then rotate. The result is the same.

What is a scalar multiplication in geometry?

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar). Scalar multiplication of a vector by a factor of 3 stretches the vector out.

What is the geometric interpretation of scalar multiplication?

In other words, multiplication by a scalar magnifies or shrinks the length of the vector by a factor of |k|. If |k|1, the length of the resulting vector will be magnified. If |k|

What is the geometric interpretation of the scalar product?

Geometrical Interpretation of Scalar Product From the scalar product formula, we have a.b = |a| |b| cos = |a| projb(a) proj b ( a ) , that is, the scalar product of vectors a and b is equal to the magnitude of vector a times the projection of a onto vector b.

What is geometric multiplication?

Geometric multiplication is a practical method of learning and practicing long multiplication using graph paper. The video lesson demonstrates how to perform the operations of multiplication by making a checkboard. This method is a fun and interactive way of developing the childs logical thinking.

What is the geometrical interpretation of AXB?

The cross product a b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.

What is geometrical interpretation of matrix multiplication?

For understanding matrix multiplication there is the geometrical interpretation, that the matrix multiplication is a change in the reference system since matrix B can be seen as a transormation operator for rotation, scalling, reflection and skew.