1.1 Intro to Geometry Flashcards
Where and When did Geometry develop?
Geometry developed with the Ancient Greeks
Who is the father of Geometry?
Euclid
- Created The Elements (13 book series of all geometrical knowledge)
- Created the basic structures of geometry which led to the creation of the Axiomatic System
What did Rene Descartes do?
Created the field of analytic geometry using algebraic expressions to define lines and curves in a coordinate system.
What was Girad Desgargues famous for?
Invented perspective geometry (lines on a converging point)
What did Leonhard Eluer do?
In the 18th century Leonhard Euler and Carl Gauss developed differential geometry (geometry of curved surfaces)
Who was Katherine Johnson and what did she do?
Katherine Johnson was a slay girl boss in the 19 century who applied geometry to calculate trajectories for NASA
Who was Benoit Mandelbrot?
A dude who used computers to develop fractal geometry
Who was Maryam Mirzakhan?
A queen who was awarded the Fields Medal in 2014 for her work with proofs on complex functions
What are the terms of the Axiomatic System?
- Undefined Terms
- Definitions
- Axioms or Postulate
- Conjectures
- Theorems
What are Undefined Terms?
Basic ideas that are defined by their name: plane, point, line
What are Definitions?
Terms that are described using undefined terms: segment, ray, angle
What are Axioms/Postulates?
a basic statement that is considered true without proof (an accepted fact)
What are Conjectures?
An idea or statement that that hasn’t yet been proven
What are Theorems?
Theorems are statements that have been proven true by use of axioms, definitions, undefined terms and other Theorems.
What is a Proof?
Proof: A logical deduction made by a Theorem
Between two points there is a _______
Positive distance
How do you tell the difference between points on a line?
Take the absolute value of the difference of the corresponding point numbers
What is the Ruler Placement Postulate?
Given that A is zero on a line, B will always be positive.
Lines are …
- One Dimensional
- Have at least two points
Planes are …
- Two Dimensional
- Have at least three points on different lines
Space is…
- Three Dimensional
- Has at least 4 points on different planes
Any three points can lie on one or more planes. Any three points that are not on the same line …..
- can only lie on one plane
The intersection of two planes…
- is a line
