科目名稱

`科目名稱`	`非歐幾何`
`授課教師`	`全任重`
`教室`	`綜三數圖電腦室`
`辦公室`	`綜三629`
`電話`	`3029`
`網頁`	http://poncelet.math.nthu.edu.tw/disk3/non-euclidean/
e-mail	jcchuan@math.nthu.edu.tw
`使用軟體`	Cabri Geometry
`評分原則`	`網頁的表現、上課的表現`

課程內容
9/13	Introduction, Cabri Geometry, Pappus Theorem, Pascal's Theorem
9/18	typhoon
9/20	inversion, construction of inversion using the comapss alone, orthogonal circles, d-line, compass under the Poincare's model, four-circle theorem
9/25	Inclusion of cabrijava to the webpage, Theorem of a Chain of Four Tangential Circles, exercise: given three points, construct three mutually tangent circles having these points as centers.
9/27	Common Tangent Circles of Two Given Circles
10/2	Pascal Theorem in conics, Brianchon's Theorem, Pappus Theorem under the Poincare's model, Pascal's Theorem under the Poincare's model, locus of the center of the common tangent circle to two fixed circles under the Poincare's model, formation of conics through paper-folding under the Poincare's model
10/4	degenerate cases of Briancheon's theorem, applications in the construction of conics: 1) given five tangents; 2)given five points; 3) given one tangent, the point of contact and three other points
10/9	creation of webpage, inclusion of CabriJava applets, Apollonius circles
10/11	conic from four points and one tangent
10/16	Theorem of Desargues, triangles in perspective,
10/18	inverse of circle and straight line, pole, polar, principle of duality, Polar line of a point with respect to a triangle
10/23	doubly perspective triangles, Theorem on triply perspective triangles
10/25	Monge's theorem
10/30	isogonal conjugates, Centers,
11/1	coaxal circles, orthogonal circles. Projective geometry, Harmonic rangle, Harmonic properties of the quadrangle and quadrilateral, cross-ratio, horocycle, hypercycle, incenter, centroid, ex-center, circumcenter, orthocenter, radical axis, 3-circle theorem, 4-circle theorem, Triangle Centers
11/6	upper half-plane model, moebius transformation
11/8	consturctions under the Poincare's model
11/13	length
11/15	symmedian point
11/20	Gergonne point
11/27	Nagal point
11/29	butterfly theorem
12/4	Conics in Poincare's model
12/6	Conics in Poincare's model
12/11	Steiner's Porisms
12/13	special cases and generalized cases of Steiner's Porism
12/25	Poncelet's Porism
12/27	special cases and generalized cases of Poncelet's Porism
1/3	Results hold true under both geometries

最新版的Cabrijava	cabrijava.jar	hyperbol.men
簡史	諮詢中心	cabriweb.jar.zip
參考資料 1	參考資料 2	參考資料 3
Inquiry-Based Lessons in Geometry

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