2006恒隆數學獎獲獎論文集（簡體書）

《2006恒隆數學獲獎論文集》不僅可供中學生閱讀，亦可供數學教師和數學愛好者閱讀參考。

Preface
by Professor Shing—Tung Yau and Mr.Ronnie C.Chan
Acknowledgement
Hang Lung Mathematics Awards
Organization
Scientific Committee，2006
Steering Comminee,2006
Gold，Silver，and Bronze
HOW TO KEEP WATER COLD A STUDY ABOUT THE WET
CONTACT SURFACE AREA IN CYLINDER
ON THE PRIME MUMBER THEOREM
CONSTRUCTION OF TANGENTS TO CIRCLES IN POINCARE MODEL
Photos
Honorable Mentions
CIRCLE PACKING
AN INVESTIGATION IN SECRET SHARING
TWO INTERESTING MATHEMATICS GAMES
ROLLING WITHOUT SLIDING
DECRYPTING FIBONACCI AND LUCAS SEQUENCES
DEVELOPING 3D HUMAN MODEL BY USING MATHEMATICAL TOOLS

When we started to do our project,we tried to investigate whether the theorems in geometry we have learnt in school are true in non—Euclidean geometry.Lacking time and background knowledge,we chose to work on Poincaré disk model of hyperbolic geometry first,instead of proving or disproving those theorems in general situations.
In the course of our work,we used Excel to calculate the Cartesian equations of hyperbolic lines and circles.This helped US find easily that many theorems about circles are not valid in Poincaré model.We were also interested in the existence of Euler line and nine—point circle.but found that both do not exist.
Our interest then shifted to construction problems.We learnt methods to construct hyperbolic lines（dlines）and circles using Euclidean com pass and straightedge,from"Compass and Straightedge in the Poincaré Disk"written by Chaim Goodman—Strauss.Bearing in our minds that in Poincaré model,circles were Euclidean circles while lines were circular arcs,we thought that the construction problems of tangents to circles in Poincarémodel should be interesting.
We have solved three construction problems by Euclidean compass and straightedge in our project,namely.
1.construction of the tangent to a circle at a point.
2.construction of the tangents to a circle from an external point.
3.construction of the four common tangents to two circles.
In the process,we tried to imitate those methods used in Euclidean geometry to construct tangents to circles.But the methods we use in Euclidean geometry require the fact that the angle in a semi—circle is a right angle,which is not true in non—Euclidean case.Finally,we developed the method of construction in a totally different way.