Exploring Advanced Euclidean Geometry with GeoGebra

Mathematical Association of America (MMA) မွ ထုတ္ေ၀ေသာ စာအုပ္ျဖစ္ပါသည္။ Geometry သင္ၾကားေရး ဆရာမ်ားကို ကို computer lab ႏွင့္ ခ်ိတ္ဆက္၍ geometry သင္ခန္းစာမ်ား ကို သင္ေပးႏိုင္ရန္ ရည္ရြယ္ ေရးသားထားေသာ စာအုပ္ျဖစ္ပါသည္။ 

Advanced Euclidean Geometry ကို Dynamic Geometry Software ျဖစ္ေသာ Geogebra ကို သံုး၍ 
ကိုယ္တိုင္ပံုဆြဲ ေျဖရွင္းေစျခင္းျဖင့္  နားလည္မႈလြယ္ကူလာေစရန္၊ ေလ့က်င့္မႈမွ ဆက္၍ tools မ်ားကို ကိုယ္တိုင္ဖန္တီးၿပီး advanced problems မ်ားကို ေျဖရွင္းတတ္ေစရန္ ရည္ရြယ္ေရးသားထားေသာ Foundation Textbook ျဖစ္ပါသည္။

Theorem မ်ားကို Mathematical proof မလုပ္ပဲ practical diagram မ်ားမွ သိရွိနားလည္လာေစရန္ ဦးစားေပးထားေသာ စာအုပ္ျဖစ္ပါသည္။ 

Book Name : Exploring Advanced Euclidean Geometry with GeoGebra
Author :  Gerard A. Venema
Content :
0 A Quick Review of Elementary Euclidean Geometry 0.1 Measurement and congruence
0.2 Angle addition
0.3 Triangles and triangle congruence conditions
0.4 Separation and continuity
0.5 The exterior angle theorem
0.6 Perpendicular lines and parallel lines
0.7 The Pythagorean theorem
0.8 Similar triangles
0.9 Quadrilaterals
0.10 Circles and inscribed angles
0.11 Area 1 The Elements of GeoGebra 1.1 Getting started: the GeoGebra toolbar
1.2 Simple constructions and the drag test
1.3 Measurement and calculation
1.4 Enhancing the sketch 2 The Classical Triangle Centers 2.1 Concurrent lines
2.2 Medians and the centroid
2.3 Altitudes and the orthocenter
2.4 Perpendicular bisectors and the circumcenter
2.5 The Euler line 3 Advanced Techniques in GeoGebra 3.1 User-defined tools
3.2 Check boxes
3.3 The Pythagorean theorem revisited  4 Circumscribed, Inscribed, and Escribed Circles 4.1 The circumscribed circle and the circumcenter
4.2 The inscribed circle and the incenter
4.3 The escribed circles and the excenters
4.4 The Gergonne point and the Nagel point
4.5 Heron’s formula 5 The Medial and Orthic Triangles 5.1 The medial triangle
5.2 The orthic triangle
5.3 Cevian triangles
5.4 Pedal triangles 6 Quadrilaterals 6.1 Basic definitions
6.2 Convex and crossed quadrilaterals
6.3 Cyclic quadrilaterals
6.4 Diagonals 7 The Nine-Point Circle 7.1 The nine-point circle
7.2 The nine-point center
7.3 Feuerbach’s theorem .8 Ceva’s Theorem 8.1 Exploring Ceva’s theorem
8.2 Sensed ratios and ideal points
8.3 The standard form of Ceva’s theorem
8.4 The trigonometric form of Ceva’s theorem
8.5 The concurrence theorems
8.6 Isotomic and isogonal conjugates and the symmedian point 9 The Theorem of Menelaus 9.1 Duality
9.2 The theorem of Menelaus 10 Circles and Lines 10.1 The power of a point
10.2 The radical axis
10.3 The radical center 11 Applications of the Theorem of Menelaus 11.1 Tangent lines and angle bisectors
11.2 Desargues’ theorem
11.3 Pascal’s mystic hexagram
11.4 Brianchon’s theorem
11.5 Pappus’s theorem
11.6 Simson’s theorem
11.7 Ptolemy’s theorem
11.8 The butterfly theorem 12 Additional Topics in Triangle Geometry 12.1 Napoleon’s theorem and the Napoleon point
12.2 The Torricelli point
12.3 van Aubel’s theorem
12.4 Miquel’s theorem and Miquel points
12.5 The Fermat point
12.6 Morley’s theorem 13 Inversions in Circles 13.1 Inverting points
13.2 Inverting circles and lines
13.3 Othogonality
13.4 Angles and distances 14 The Poincar´e Disk 14.1 The Poincar´e disk model for hyperbolic geometry
14.2 The hyperbolic straightedge
14.3 Common perpendiculars
14.4 The hyperbolic compass
14.5 Other hyperbolic tools
14.6 Triangle centers in hyperbolic geometry