Module 6 Flashcards
“Geometry” from two greek words geo and metron which mean _____ and _____
earth, measurement
How many clay tablets were unearthed containing Babylonian Mathematics?
400
What was Babylonian Mathematics written of?
Cuneiform script
Who gave us the formulas for finding areas and volumes of some geometric figures like circles and cylinders?
The Babylonians
What was Ahmes Papyrus also know of?
Rhind Mathematical Papyrus
This value is what we call the golden ratio.
1.618
What do in literature call when the rectangles having the ratio of length and its width be golden ratio
golden rectangles
First mathematician to calculate the circumference of the earth
Eratosthenes
Who gave us the concept that given a right triangle with lenghts of ides a and b; and, length of side opposite the right angle is c, then a² + b² = c²?
Pythagoras
Who contributed a handful geometric concepts like the volumes of irregular shapes?
Archimedes
He was also known for deriving an accurate approximation of the value π using the meyhod of exhaustion developed by Eudoxus of Cnidus
Archimedes
One of the most famous Greek mathematicians
Euclid
Things that are equal to the same thing are ____
equal
If equals are added to equals, then the ____ are equal
whole
if equals are subtracted from equal, then the ____ are equal
remainders
things that ____ with one another are equal to one another
coincide
The ____ is greater than the part
whole
a straight line can be drawn from any point to any point
Postulate 1
A finite straight line can be produced continuously in a straight line
Postulate 2
A circle may be drawn with any point as center and any distance as radius
postulate 3
All right angles are equal to one another
Postulate 4
The 5th postulate is also called
Parallel Postulate
Two lines are equidistant
Posidonius
If a line intersects one of two parallel lines, then it intersects the other
Proclus
The sum of the interior angles of a (Euclidean) triangle is 180
Legendre
He restated Euclid’s 5th Postulate as “Through a point P not on line l, there exists exactly one line passing through point P parallel to l”
Playfair
Two Euclidean triangles are congruent if only if they the
same size and shape
Two triangles are similar if they have the same
shape but can be different sizes
a model for this hyperbolic geometry can be seen by considering not the usual plane, but a ____
circular disk
Who were the main contributors of Hyperbolic Geometry?
Nikolai Ivanovich Loba Chevsky
Janos Bolyai
Johann Carl Friedrich Gauss
what is the point of hyperbolic?
usual points inside the disk (but not lying on the boundary)
The sum of the angles of a triangle is less than 180°
Hyperbolic
The sum of the interior angles of a triangle is more than 180°
Elliptic
Known as the father of projective geometry
Gerard Desargues
Gerard considered the concept of parallel lines intersecting in a plane and called this the
ideal point
The point of intersection is called the
center of perspectivity
A coffee cup and a muffin
NOT topologically equivalent
Coffee cup and donut
Topologically equivalent
All congruent trianges are similar. This is true in what type of geometry?
Elliptic, Hyperbolic and Euclidean
Through a point P not on line l, there exists more than one line passing through point P parallel to l
Hyperbolic
Topology includes the mathematical study of vanishing points and perspective
False
