问题1.绘制一个示意图以说明以下内容。
(i)开放曲线
(ii)闭合曲线
解决方案：
i)开放曲线：起点和终点不相交的曲线称为开放曲线。
ii)闭合曲线：起点和终点彼此相交或彼此切割的曲线称为闭合曲线。
问题2.将以下内容分类为“开放”或“封闭”。
解决方案：
- open curve: A curve in which starting point and ending point are different or do not cut each other .
- closed curve: A curve in which starting point and ending point are same and cut each other.
Using the above definition we can classify the given figures as follows :
i) open curve (as both stating and ending points are diffrent)
ii) closed curve (as both the points are same )
iii) closed curve (as both the points cut each other)
iv) open curve (as both starting point and ending point are diffrent)
v) open curve (as both starting point and ending point are diffrent)
vi) closed curve (as both starting point and ending point meet at same point)
问题3.绘制一个多边形并将其内部着色。还要绘制其对角线(如果有)：
解决方案：
在多边形ABCD中，AC和BD是多边形的对角线
问题4.如果可能的话，请用粗略图说明以下各项。
(i)不是多边形的闭合曲线。
(ii)一条完全由线段组成的开放曲线。
(iii)具有两个边的多边形。
解决方案：
(i)不是多边形的闭合曲线。
(ii)一条完全由线段组成的开放曲线。
(iii)具有两个边的多边形。
A polygon with two sides is not possible because, a polygon should have minimum three sides.
问题5.以下是一些数字：根据以下各项对每个数字进行分类：
(i)简单曲线
(ii)简单闭合曲线
(iii)多边形
(iv)凸多边形
(v)凹面多边形
(vi)不是曲线
解决方案：
(i) It is a Simple Closed curve and a concave polygon. This is a simple closed curve and as a concave polygon all the vertices are not pointing outwards.
(ii) It is a Simple closed curve and a convex polygon. This is a simple closed curve and as a convex polygon all the vertices are pointing outwards.
(iii) It is Not a curve and hence it is not a polygon.
(iv) It is Not a curve and hence it is not a polygon.
(v) It is a Simple closed curve but not a polygon.
(vi) It is a Simple closed curve but not a polygon.
(vii) It is a Simple closed curve but not a polygon.
(viii) It is a Simple closed curve but not a polygon.
问题6.以下每个对角线有多少对角线?
(i)凸四边形
(ii)正六边形
(iii)一个三角形
解决方案：
i)凸四边形
For a convex quadrilateral we shall use the formula n(n-3)/2
So, number of diagonals = 4(4-3)/2 = 4/2 = 2
A convex quadrilateral has 2 diagonals.
(ii)正六边形
For a regular hexagon we shall use the formula n(n-3)/2
So, number of diagonals = 6(6-3)/2 = 18/2 = 9
A regular hexagon has 9 diagonals.
(iii)一个三角形
For a triangle we shall use the formula n(n – 3)/2
So, number of diagonals = 3(3 -3)/2 = 0/2 = 0
A triangle has no diagonals.
问题7.什么是规则多边形?指出的正多边形的名称
(i)3面
(ii)4面
(iii)6面
解决方案：
Regular Polygon: A regular polygon is an enclosed figure. In a regular polygon minimum sides are three.
(i) 3 sides
A regular polygon with 3 sides is known as Equilateral triangle.
(ii) 4 sides
A regular polygon with 4 sides is known as Rhombus.
(iii) 6 sides
A regular polygon with 6 sides is known as Regular hexagon.