Euclidian geometry beginner vocab

Started reading a book about Geometry and learned a few basic vocab items in Euclidean Geometry for the first time, including points, lines (and rays, segments), planes and collinear/coplanar. Oh and "between".

Sep 10, 2024

Tonight, I started reading the book Geometry by Construction.

This was prompted by not being able to figure out how to design a 2D pyramid-shaped funnel for my skittle sorting robot.

I asked ChatGPT what concepts I'd need to know to learn how to design the funnel piece, and it said I'd need to know:

  • Basic trigonometry to calculate the slant angle of the trapezoidal sides (side of pyramid like funnel).
  • Area and perimeter to make sure the sides match up properly
  • The Pythagorean theorem for the slant height.

Usually, I'd just try and learn those things to help me move forward without trying to really pick up the foundations. Buut, something about learning Geometry, really learning it, appeals to me.

So here we are!

I have this basic geometry set from Amazon:

And this beautiful Hahnemuhle Nostalgie A5 190gsm Landscape Sketch Book. Plus a set of my favourite Sakura pigma micron pens (size 03).

The materials add to the joy of sketching and working through these ideas, because they feel so delightful to use.

Basic vocab for Euclidean Geometry (pt 1).

Anyway, in todays session, I learned some super beginner basic vocab for Euclidean Geometry.

Also also, I was today years old when I found out I can copy text on my iPad (kindle), and PASTE IT STRAIGHT IN MY PHONE. It blew my mind 🤯 I pasted the line definition paragraph into ChatGPT and asked it to break it down and give examples because it went right over my head. It helped.

  • Point: A pure location, no size or dimension. This marks the spot.
  • Line: Extends infinitely in one direction, no start or end points. One-dimensional; They have a length but not a width or depth.
  • Ray: Extends infinitely in one direction, and has a starting point.
  • Segment: A piece of a line with a start and an end point.
  • Collinear: Several points that all sit on the same line. If you were to draw a line that passes through all points, they are collinear.
  • Plane: A flat, 2D surface that extends infinitely in all directions. Like an infinite piece of paper.
    • A plane can be defined by any 3 or more points that are not collinear (like the points of a triangle).
    • A plane can be defined by two intersecting lines. Think of an X, where the lines are touching as they cross-over. This is still a bit confusing to me.
  • Coplanar: Where several points and or lines are on the same flat surface as each other.
  • Between: Point B lies between point A and C, if the distance between A and C is the same as the distance between (point A plus B) plus (point B plus C).

I traced around all the rulers and compasses etc in my geometry set, then scribbled these definitions on top of it.

Remaining concepts to learn in the vocab section are divided into:

  • Isometrics
  • Special lines
  • Special angles
  • Bisectors
  • Circles
  • Triangles
  • Quadrilaterals

These are the foundational concepts that underpin everything else in the entire book. So I want to make sure I fully understand them, and maybe put them into a flashcard app to help me memorize them via spaced repetition.

This is a good start!