We're Making New Math??

In this world... There Exist (the magic words in math)
A Face Position of a shape (a shape's 2 dimensional view)
A Line Position of a shape (the projection of the shape into a one dimensional line)
A Line Position Value (the length of the projection of the shape in line position)
LPV changes based on shape and rotation angle of the shape (so there is a notation specifying the shape and its rotation, with the flat side of a shape positioned parallel to the x axis is denoted as 0 degrees where applicable)

Shapes are considered the same if they have the same line position value
At face position, the shape can be changed (to any other shape with the same LPV)
At line position, a shape may be rotated by any amount of degrees

Things we found:
LPV differs with shapes. A circle has a constant LPV, while other shapes like squares and triangles have varying LPVs.
A circle with diameter D can be transformed into a larger circle with diameter D*sqrt(2) in 3 transformations.
Each shape has an LPV pair, made up of a max and min LPV. That max and min can be transformed into a ratio (Min/Max).
Is there a unique ratio for each shape based on its max and min LPV? No! Because we have a counter example = the ratio for a triangle shape is the same as for a hexagon shape.
Some ratios are constant, others have a range dependent on the side lengths of the shape.

My Questions for me:
How to find the area of a triangle without knowing it's height?
How to re-write the formula of an octagon just in terms of the denoted x.

My Questions for you:
In your opinion, what parts of this first attempt at explaining were good, what parts need work?
If you got lost, was there a particular location where you started to get lost?
What other questions can you come up with that we can ask in this world of math?

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Hey :) Grab your beverage of choice and join me for some math explorations! You know the deal, this is unscripted, unscheduled, organized chaos! This video is my first attempt at explaining the new math world my friend and I have been playing around with. (There's a chance as I get more familiar with it, I'll be able to explain it better).

Concepts it would be helpful to be familiar with to follow along with this video: The Pythagorean theorem, square roots, angles, 108 degrees in a triangle, coordinate plane.

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Hi!
Thanks for watching :)
I'm Janet, the Architect of Ideas and aspiring Unofficial Professor of Patterns... creativity and curiosity drive my life.

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