5.1 Elementary Geometry: Co Linear and Concurrent Points

Colinear points are those that lay on one line.

Concurrent points are those lines that intersect at a single point.

There is a Placement or Rhythm of Movement of points along a line, just as in music there are notes. Vertical line placement can be expressed on a scale of musical notes.

The reflection of this concept in Dance and Design is both rhythm of movement (movement and lack of movement) in any straight direction or line: up, down, side-to-side, or horizontal.

Mathematics Day 5.2: Elementary Geometry: Pascal’s Theorem: What is a Theorem?

What is a Theorem? What is Pascal’s Theorem in elementary Geometry?

A Theorem is an evident pattern in nature or natural phenomenon that can be shown to exist (proven) with mathematics.

We have not discovered all of the patterns of Nature in the Science of Mathematics, so Mathematicians are always looking to discover new patterns, and to prove them. Once they have been proven, they are called a Theorem.

Remember: a scientist makes a hypothesis based on his question or curiosity. Then he or she does the experiments to discover if the hypothesis is true. Once a hypothesis can be proven it is called a Theory. In Mathematics, it is called a Theorem.

Pascal’s Theorem is expressed as follows:

Consider 6 points on a circle. Define them A, B, C and A’, B’ and C’. You will discover (AB’) (A’B) (BC’) (B’C) (AC’) (A’C)

You can see this for yourself by putting the 6 points on a circle, drawing the lines as above and noting the intersecting points. They are co-linear or all on the same line.

Kinesthetically, this can be expressed by tracing these lines on a grid and forming various geometric patterns.

New Children: Educational Kinesiology: Fundamental Geometry: Projective Line Geometry