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. Theorems that apply to the 1st, second or third dimension can be seen in our physical/material world. Other dimensions or realities an be proven mathematically, but we may have not seen them evident.

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.

This pattern is easily observable in nature, it is reflected in art and even music and musical rhythm.

Applied Kinesiology (applied science of movement)

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

*About me: I am Tara, the writer of these blogs about education and specifically mathematics. I am a (primary-middle school) teacher. I am interested in having accurate materials and teaching methods. By composing this series of mathematics lessons, I am preparing for my classes. I am also a dancer. It is hard for me to sit in one place. It is easier for me to learn with movement, color, examples and ideas. According to research 60% of children learn kinesthetically, like I do. I hope to be an Educator who has developed a way to provide this service of kinesthetic learning for others.I also hope to find the philosophical answer to this question: “WHY I am doing mathematics in the first place? Discovering the answer to this question has sent me on an adventure to learn the fundamentals of nature and our universe as expressed in mathematical language. “God is universal harmony perceived through numbers.” – Pythagoras *

*xo Tara Pelton*