SHAPES

• The laws of nature are but the mathematical thoughts of God


  what is Euclid's quote?
• Father of Geometry


  What is Euclid known as?
• as a practical way of dealing with AREAS, LENGTHS, and VOLUMES


  why was geometry developed?
• Geo and Metron (earth and measurement)


  From what Greek words did the term "Geometry" came from?
• The Elements


  What made Euclid be the "Father of Geometry"
• 13


  how many volumes does Euclid's book has?
• Greek, Latin, Arab


  Order of translations of Euclid's Book
• from basic assumptions, axioms, or postulates, then he deduced theorems from it


  how did Euclid started his book?
• deduce theorems from axioms


  what has no one done before that Euclid eventually did?
• not reading Euclid's book


  what makes people "uneducated" back then?
• second most printed book after Bible


  Euclid's book was the ____ most printed book
• to tighten our reasoning and proving


  why study geometry?
• making some assumptions and deducing from those assumptions


  what is Euclidian's Geometry all albout?
• 400 tablets containing Babylonian Mathematics written in cuneiform script


  during 1850s, what were unearthed?
• formulas for finding areas and volumes of circles and cylinders


  what did Babylonian math gave us?
• 3


  what was the value of pi during the Babylonian?
• C= 3 x diameter and A =1/12 C^2

  what was the formula deduced by the Babylonians?
• their famous pyramids


  what were constructed during the Egyptian civilization?
• determination of food supply


  what were determined during the Egyptian civilization?
• Ahmes Papyrus or Rhind Mathematical Papyrus

  from what material was the Egyptian civilization records?
• eratosthenes


  Known to be the first mathematician to calculate the circumference of the earth.
• c^2= a^2 + b^2


  formula of Pythagorean Theorem
• right triangle


  on what triangle is the Pythagorean theorem applied to?
• Archimedes of Syracuse


  who derived the approximate value of pi
• using the method of exhaustion by Eudoxus of Cnidus


  how did Archimedes derived the approximate value of pi?
• the volumes of irregular shapes


  what did Archimedes of Syracuse determined?
• golden rectangles, and irrational numbers like the radical, pi, and golden ratio


  what are the most significant contributions of the Greeks
• 1.618


  what is the approximate value of golden ratio?
• A straight line can be drawn from any point to any point.


  Postulate 1 of Euclid's Postulate
• A finite straight line can be produced continuously in a straight line.


  Postulate 2 of Euclid's Postulate
• A circle may be drawn with any point as center and any distance as radius.


  Postulate 3 of Euclid's Postulate
• All right angles are equal to one another.


  Postulate 4 of Euclid's Postulate
• If a transversal falls on two lines in such a way that the interior angle on one side of a transversal are less than two right angles, then the lines meet on that side on which the angles are less than two right angles.


  Postulate 5 of Euclid's Postulate
• same size and shape


  what is congruent?
• same shape


  what is similar?
• 180


  what is the sum of the measures of the interior angles of any euclidean triangle
• triangle


  what is the most stable shape?
• congruent triangles are similar but not vice versa


  what did it say about congruent and similar triangles?
• less than 180


  the sum of the angles of a (hyperbolic) triangle is
• more than 180


  the sum of the interior angles of (an elliptic) triangle is