
EUCLIDEAN GEOMETRY 26 AUGUST 2013 Key Concepts
... Geometry is divided into Euclidean geometry and analytical geometry. Analytical geometry deals with space and shape using algebra and a coordinate system. Euclidean geometry deals with space and shape using theorems and a system of logical deductions, as developed by the Greek mathematician Euclid. ...
... Geometry is divided into Euclidean geometry and analytical geometry. Analytical geometry deals with space and shape using algebra and a coordinate system. Euclidean geometry deals with space and shape using theorems and a system of logical deductions, as developed by the Greek mathematician Euclid. ...
Geometry of 2D Shapes - E
... State wether the following statements (sentences are true or false). If the sentence is false, change it to make the sentence true. a) All squares are rectangles. b) All rhombuses are parallelograms. c) All trapeziums are parallelograms. d) All kites are rhombuses. e) All rectangles are squares ...
... State wether the following statements (sentences are true or false). If the sentence is false, change it to make the sentence true. a) All squares are rectangles. b) All rhombuses are parallelograms. c) All trapeziums are parallelograms. d) All kites are rhombuses. e) All rectangles are squares ...
Sample Space
... Ex3) You can use a grid instead of tree if the sample space will be large. Rolling two dice. Outcomes = 36 ...
... Ex3) You can use a grid instead of tree if the sample space will be large. Rolling two dice. Outcomes = 36 ...
3-3 Notes
... 3-3 Proving Lines Parallel Example 1A: Using the Converse of the Corresponding Angles Postulate Given the information to show that ℓ || m. ...
... 3-3 Proving Lines Parallel Example 1A: Using the Converse of the Corresponding Angles Postulate Given the information to show that ℓ || m. ...
Chapter 2 Vocabulary/ Postulate/Theorem Test
... 1. A ______________ is the simplest unit in geometry. 2. _______________is the set of all points. 3. The common endpoint of the rays on an angle is called the _______________. 4. _______________________ have a common vertex and common side, but no common interior points. 5. If…, then…. can be called ...
... 1. A ______________ is the simplest unit in geometry. 2. _______________is the set of all points. 3. The common endpoint of the rays on an angle is called the _______________. 4. _______________________ have a common vertex and common side, but no common interior points. 5. If…, then…. can be called ...
When is it appropriate to use a Combination or a Permutation?
... How many ways can you shuffle a deck of cards? How many bridge hands are possible? (set of 13 cards) How many NC license plates are there? (3 letters and 4 numbers) How many phone numbers are in an area code? MULTIPLICATION RULE: When something is done in operations (stages or steps), the to ...
... How many ways can you shuffle a deck of cards? How many bridge hands are possible? (set of 13 cards) How many NC license plates are there? (3 letters and 4 numbers) How many phone numbers are in an area code? MULTIPLICATION RULE: When something is done in operations (stages or steps), the to ...
3-3 Proving Lines Parallel
... 6. Vert.∠s Thm. 7. Substitution 8. Conv. of Same-Side Interior ∠s Post. ...
... 6. Vert.∠s Thm. 7. Substitution 8. Conv. of Same-Side Interior ∠s Post. ...
Geometry and Proof: Course Summary
... The main claim of the course is that the choices of axiom system seriously impact what students can learn in the geometry class. If the real numbers are built into the system there is a temptation to insist on very pedantic proofs of trivial ...
... The main claim of the course is that the choices of axiom system seriously impact what students can learn in the geometry class. If the real numbers are built into the system there is a temptation to insist on very pedantic proofs of trivial ...
4 Designing digital technologies and learning activities for different
... a key idea. Work by Euler, Wolfgang and Janos Bolyai, and Lobachevskii, to name but a few, showed that Euclidean geometry was one of many possible geometries: its uniqueness lay with its ‘flatness’, not, as Kant would have it, because it is ‘absolute’. Curvature, as a geometric property, and because ...
... a key idea. Work by Euler, Wolfgang and Janos Bolyai, and Lobachevskii, to name but a few, showed that Euclidean geometry was one of many possible geometries: its uniqueness lay with its ‘flatness’, not, as Kant would have it, because it is ‘absolute’. Curvature, as a geometric property, and because ...
Space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates in his reflections on what the Greeks called khôra (i.e. ""space""), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later ""geometrical conception of place"" as ""space qua extension"" in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath Alhazen. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the ""visibility of spatial depth"" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant said that neither space nor time can be empirically perceived—they are elements of a systematic framework that humans use to structure all experiences. Kant referred to ""space"" in his Critique of Pure Reason as being a subjective ""pure a priori form of intuition"", hence it is an unavoidable contribution of our human faculties.In the 19th and 20th centuries mathematicians began to examine geometries that are not Euclidean, in which space can be said to be curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.