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

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

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, degenerate cases of Briancheon's theorem, principle of duality, pole, polar, coaxal circles, orthogonal circles. inverse of circle and straight line, Projective geometry, Theorem of Desargues, triangles in perspective, Polar line of a point with respect to a triangle, Harmonic rangle, Harmonic properties of the quadrangle and quadrilateral

10/4

cross-ratio

10/9

doubly perspective triangles

10/11

Monge's theorem

10/16

Theorem on triply perspective triangles

10/18

horocycle, hypercycle

10/23

Centers, incenter, centroid, ex-center, circumcenter, orthocenter

10/25

isogonal conjugates

10/30

radical axis, 3-circle theorem, 4-circle theorem

11/1

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

學號 

姓名 

所系班別 

870260 戴劍英 數學系四年級純數組
893208 曾俊榮 數學系碩士班純數組
893212 侯杰材 數學系碩士班純數組
903206 黃彥彰 數學系碩士班純數組
903254 楊澤璿 數學系碩士班應數組
903264 吳偉弘 數學系碩士班應數組