With the given notes from below, answer number one please Axiom 1: there exists at least one line...
With the given notes from below, answer number one please
Axiom 1: there exists at least one line.
Axiom 2: every line has exactly 8 points incident (passes through) to it
Axiom 3: not all points are incident to the same line
Axiom 4: there is no line containing all points
Axiom 5: there is at least two points on one line
Axiom 6: there exists at least two lines
Axiom 7: there is exactly on with incident with any two discount points
Axiom 8: there is at least on point incident with any two distinct lines
1A) Is this system categorical or not?
1B) What is the situation vis a vis parallel lines? (using Playfair)
1C) Is this geometry elliptical, hyperbolic or Euclidean with respect to parallel lines?
Homework Answers
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With the given notes from below, answer number one please Axiom 1: there exists at least one line...
Part II. (4 pts) Given the axiom set for the Incidence Geometry as below: Undefined terms: point, line, on Definitions: 1. Two lines are intersecting if there is a point on both. 2. Two lines are...
Part II. (4 pts) Given the axiom set for the Incidence Geometry as below: Undefined terms: point, line, on Definitions: 1. Two lines are intersecting if there is a point on both. 2. Two lines are parallel if they have no point in common. Axioms: I. Given any two distinct points, there is a unique line on both. II. Each line has at least two distinct points on it. III. There exist at least three points. IV. Not all points...
using these axioms prove proof number 5 1 - . Axiom 1: There exist at least...
using these axioms prove proof number 5
1 - . Axiom 1: There exist at least one point and at least one line Axiom 2: Given any two distinct points, there is exactly one line incident with both points Axiom 3: Not all points are on the same line. Axiom 4: Given a line and a point not on/ there exists exactly one linem containing Pouch that / is parallel tom Theorem 1: If two distinct lines are not parallet,...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one additional a...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one additional axiom added: Incidence Axiom l: For every point P and every point Q (P and Q not equal), there exists a unique line, I, incident with P and Q. Incidence Axiom 2: For every line / there exist at least two distinct points incident with Incidence Axiom3: There exist (at least) three distinct points with the property that no line is incident with...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one additional axiom added: Incidence Axiom l: For every point P and every point Q (P and Q not equal), there exists a unique line, I, incident with P and Q. Incidence Axiom 2: For every line / there exist at least two distinct points incident with Incidence Axiom3: There exist (at least) three distinct points with the property that no line is incident with...
Duality Axiom 1. There exist exactly 4 distinct points. Axiom 2. There exist exactly 5 distinct...
Duality
Axiom 1. There exist exactly 4 distinct points. Axiom 2. There exist exactly 5 distinct lines. Axiom 3. There is exactly 1 line with exactly 3 distinct points on it. Axiom 4. Given any 2 distinct points, there exists at least 1 line passing through the 2 points. Which of the following is the dual of Axiom 4? O a. Every line has at least 2 points on it. b. There exists at least 1 point with at least...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.] 5) Consider the following statements: I: If two triangles are congruent, then they have equal defect. II: If two triangles are similar, then they have...
3. Determine which of the following are models of Incidence Geometry. For those th are models,...
3. Determine which of the following are models of Incidence Geometry. For those th are models, indicate which parallel property holds for the model. For those that a not a model, list at least one axiom that fails and illustrate why. a. Points are points in the Euclidean plane and lines are circles with positive radius. b. Points are in {(x, y) = R2 22 + y2 <9} and lines are open chords of the circle. c. Points are points...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry, gcometry and D. for Neutral geometry for your identifications Example. A There is a triangle in which the sum of the measures of the interior angles is 180. a. The opposite sides of a parallelogram are congruent. b. Similar triangles may not be congruent. Lines perpendicular to the...
first one is example. i need to solve second picture. 3,4 picture apply to step 1...
first one is example.
i need to solve second picture. 3,4 picture apply to step 1 and 2.
that is CAD problems thanks
Objective: The following figures represent model views in an engineering drawing. First, inspect each cross-section and write down observations about the geometry le... shape is square, all rounds are equal in size, etc.). Second, determine the DOF of curves. Third, determine the DOF removed by constraints (e.8., 1 pair of parallel lines removes 1 DOF, etc.). Finally,...
Answer all of these, please Using Aplia graphs me questions will ask you to interpret a given oraph, and others will require you to manipulate the objects on the graph or even add new required...
Answer all of these, please
Using Aplia graphs me questions will ask you to interpret a given oraph, and others will require you to manipulate the objects on the graph or even add new required objects,. Each manipulable oblect will be shown in the area to the right of the praph (the palette) and referred to by ts color, object type, and shape of the control points, for example, black point (plus symbol). To place an object on the graph,...
Part II. (4 pts) Given the axiom set for the Incidence Geometry as below: Undefined terms: point, line, on Definitions: 1. Two lines are intersecting if there is a point on both. 2. Two lines are parallel if they have no point in common. Axioms: I. Given any two distinct points, there is a unique line on both. II. Each line has at least two distinct points on it. III. There exist at least three points. IV. Not all points...
using these axioms prove proof number 5
1 - . Axiom 1: There exist at least one point and at least one line Axiom 2: Given any two distinct points, there is exactly one line incident with both points Axiom 3: Not all points are on the same line. Axiom 4: Given a line and a point not on/ there exists exactly one linem containing Pouch that / is parallel tom Theorem 1: If two distinct lines are not parallet,...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one additional axiom added: Incidence Axiom l: For every point P and every point Q (P and Q not equal), there exists a unique line, I, incident with P and Q. Incidence Axiom 2: For every line / there exist at least two distinct points incident with Incidence Axiom3: There exist (at least) three distinct points with the property that no line is incident with...
3) Let us build a geometry, S, using the three axioms of incidence geometry with one additional axiom added: Incidence Axiom l: For every point P and every point Q (P and Q not equal), there exists a unique line, I, incident with P and Q. Incidence Axiom 2: For every line / there exist at least two distinct points incident with Incidence Axiom3: There exist (at least) three distinct points with the property that no line is incident with...
Duality
Axiom 1. There exist exactly 4 distinct points. Axiom 2. There exist exactly 5 distinct lines. Axiom 3. There is exactly 1 line with exactly 3 distinct points on it. Axiom 4. Given any 2 distinct points, there exists at least 1 line passing through the 2 points. Which of the following is the dual of Axiom 4? O a. Every line has at least 2 points on it. b. There exists at least 1 point with at least...
3. Determine which of the following are models of Incidence Geometry. For those th are models, indicate which parallel property holds for the model. For those that a not a model, list at least one axiom that fails and illustrate why. a. Points are points in the Euclidean plane and lines are circles with positive radius. b. Points are in {(x, y) = R2 22 + y2 <9} and lines are open chords of the circle. c. Points are points...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry, gcometry and D. for Neutral geometry for your identifications Example. A There is a triangle in which the sum of the measures of the interior angles is 180. a. The opposite sides of a parallelogram are congruent. b. Similar triangles may not be congruent. Lines perpendicular to the...
first one is example.
i need to solve second picture. 3,4 picture apply to step 1 and 2.
that is CAD problems thanks
Objective: The following figures represent model views in an engineering drawing. First, inspect each cross-section and write down observations about the geometry le... shape is square, all rounds are equal in size, etc.). Second, determine the DOF of curves. Third, determine the DOF removed by constraints (e.8., 1 pair of parallel lines removes 1 DOF, etc.). Finally,...
Answer all of these, please
Using Aplia graphs me questions will ask you to interpret a given oraph, and others will require you to manipulate the objects on the graph or even add new required objects,. Each manipulable oblect will be shown in the area to the right of the praph (the palette) and referred to by ts color, object type, and shape of the control points, for example, black point (plus symbol). To place an object on the graph,...
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