圆内接正五边形的画法
元 王蒙 青卞隐居图轴
纸本墨笔 140.6x42.2cm 上海博物馆藏
王蒙与《青卞隐居图》
《青卞隐居图》为王蒙的代表作之一,主要笔墨特点是:
1.笔法丰富,墨色层次微妙,疏荡而不病于放,绵密而不嫌于弱。体现了典型元人山水风格的“松”“糯”“毛”。
2.以渴成润,用较枯之笔层层积染皴擦,笔墨融合,温润凝净。
3.山石披麻皴、牛毛皴、解索皴交互使用,皴擦并举,山顶多作矾头。
4.树法多用点叶树,穿插枯枝、松树。
5.各种点法交互穿插使用,焦墨渴笔点多用于峰峦山脊、石嘴、顶巅、凹隙及脉络转折处,有的似皴擦似苔点交融为一。近中景、山坡、树干树叶则多用疏朗圆笔攒点,以湿墨浓重处理。
6.画法由小到大,由近到远,层层生发。
临摹提示：
1.临摹此画选用不太渗化的纸为宜(半生熟)。
2.宜用弹性较好的狼毫、精毫笔。
3.墨最好是研的。(可用中华墨汁胶较轻渗水再研过,也算便捷)。
4.动笔前,要对作品的章法、结构、形质、笔墨等细节作认真细致的观摩。
如用两周时间临摹,第一周进行较细致的读画、练笔,尽量理解画中的形体结构、组织规律及笔法、墨法规律,捕捉其沉厚郁密,灵秀洒脱的气息。体会古人十日一水,五日一石的作画心境。调整自我平静的状态。
第二周正稿临摹,自下而上,由近及远,随势生发。
树的画法
画树步骤:
①勾树干落笔要肯定,用笔要松动,以卧笔中锋连拖带写。接笔处与转折处要有笔意的呼应。
②先画主干再画次干,中枝的出枝要注意角度和姿态。树干要有组织结构。枯树先画树身左边枝,自上而下,枝梢取横势,左右两笔呈扁平“V”形,内角较大,逐个生发。要有疏密,松紧的节奏。
丘挺临王蒙《青卞隐居图》课徒稿
③当中两棵点叶树用大混点。注意笔蘸墨要考究——笔嘴墨较浓重,笔肚则淡些,笔根几乎是清水,下笔时笔尖向外,卧笔横取,在纸上稍作停留(笔与纸面大约呈40度),其墨韵的微妙变化是通过毛笔的运用及其落墨过程的浓淡相破而产生的。另,点叶树中的一些出枝,也不能马虎,只有这些出枝到位,所点的叶子才能嵌准结构。
丘挺临王蒙《青卞隐居图》课徒稿
渴笔点:全用焦墨点之,画时可在另纸将笔调整好,笔锋散开,看准应点的地方,集中精力,以腕重击桌面有声从容落下,笔头猛着画面,层层而上,要注意点与树干碰离关系。
松树画法
全用中锋笔线写出,用笔如书法中行草笔法,体会“平”“圆”的感觉,要注意笔势的回收与连贯性。
丘挺临王蒙《青卞隐居图》课徒稿
画中近景树林基本是由各种点叶树组成，关系较复杂、疏密有致,大体上树直者用横点、圆点；欹侧者用散锋渴笔点、枯树则矫然于林外,左右盼顾,若即若离。丛树整立而近边树则较翩跹。
丘挺临王蒙《青卞隐居图》课徒稿
临摹时要注意：
①树干多用长线条结合短线,笔线与笔线之间要顺势生发。
②多种点叶要注意组织、疏密、松紧、浓淡、枯湿等笔墨关系。用笔要带有写的意味,不要谨勾细描。
③同类点叶树点叶要抱紧树身、注意点叶与树干的碰让关系,一棵一棵由前到后逐次完成。
山石画法
山石画法步骤:
勾、皴、擦、染,有时也交互进行。勾勒宜用含水较少的笔头,用笔要有变化,随山石形体的走势来行笔。要有顿挫、转折的笔意。笔与笔要有碰有让。此图画法基本上是勾皴并举,边勾边皴边擦,皴笔则由石块的阴面皴起。勾皴石头注意不要笔笔勾死,不能太实(易板刻)，也不要太虚,(不见骨力),注意山石的大小、疏密相间。另,转折处忌妄生圭角。
丘挺临王蒙《青卞隐居图》课徒稿
丘挺临王蒙《青卞隐居图》（局部）
画解索皴尤贵笔意,下笔要沉着痛快,藏锋入笔,寓刚于柔,笔笔送到,忌浮滑。画时要注意笔线之间的组合关系，不要太规则,成“8”字形，要根据山脉的结构,一组一组地生发,尤贵画得“毛”“松”。
丘挺临王蒙《青卞隐居图》课徒稿
由于王蒙的解索皴颇为繁密,故练笔时要抓住皴法中“笔路”的源头,找出其自上而下的序次,由此来分辩判断其组织结构以及笔墨关系。
枯笔牛毛皴,画时自右而左,用曲屈笔线紧排旋转而出之,带篆隶笔意,笔线较短,干后用淡而润的皴笔复加,四五遍而成,亦是以渴成润法,第一遍当出效果。牛毛皴多与解索皴夹用,较少单独成幅。
丘挺临王蒙《青卞隐居图》课徒稿
丘挺临王蒙《青卞隐居图》课徒稿
这块山石属披麻破,所以运笔多带平行，但不可绝对。执笔要松、行笔要松,体会毛笔在纸上时顶住纸面欲入又不全入的感觉。披麻破三五成组，笔致与形体的凸凹相联系,凹处簸笔宜多而浓,凸处宜淡而少,笔线之间宜少交叉,要有条理,可边皴边擦连续出之。
丘挺临王蒙《青卞隐居图》（局部）
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季阅是4475怎样尺规作图画5边形 -
赵爬芸15244169871 ______[答案] 圆内接正五边形的画法如下: 作一个圆,设它的圆心为O; 作圆的两条互相垂直的直径AZ和XY; 作OY的中点M; 以点M为圆心,MA为半径作圆,交OX于点N; 以点A为圆心,AN为半径,在圆上连续截取等弧,使弦AB=BC=CD=DE=AN,则五边...
季阅是4475如何做圆的内接正五边形 -
赵爬芸15244169871 ______ 接助于这个＂黄金三角形＂就很容易有一下的结论,但是首先你应该确认上属三角形存在,不妨自己验证一下 (点击有大图) 把黄金三角形移入圆中就会发现正无边形的边长原来就是红线的二倍,根据比例就可以由半径R算出边长 根据半径和边长的比例,提供两种作圆内接无边形的方法,如下: (点击有大图) 左图侧重于作出边长,右图侧重于左角度(边所对的圆心角72度) 当然,也可以用三角函数先算出半径和正五边形的边长,再作图;利用cos72=sin18,进行合理的变化,求出cos72的值如高斯的正十七边形,它的比例关系更夸张,根号是一层又一层,相关参阅
季阅是4475怎样作圆的内接正五边形?为什么 -
赵爬芸15244169871 ______ 360/5=72 作出5个72度的圆心角,再依次连接5个交点就到得到内接正五边形.
季阅是4475怎么画正五边形 -
赵爬芸15244169871 ______ 圆内接正五边形的尺规作图 (1)以O为圆心,定长R为半径画圆,并作互相垂直的直径MN和 AP. (2)平分半径ON,得OK=KN. (3)以 K为圆心,KA为半径画弧与 OM交于 H, AH即为正五边形的边长. (4)以AH为弦长,在圆周上截得A、B、C、D、E各点,顺次连接这些点即得圆内接正五边形.
季阅是4475如何只用一个圆规就能画出圆的内接五边形 -
赵爬芸15244169871 ______[答案] 方法一:首先在纸上用圆规画个圆,然后画出圆的两条相互垂直的直径AC与BD;之后分别用C、D作圆心,用直径BD的半径作弧,两弧交在E点.则OE便近似等于圆的内接正五边形之边长.自A点开始,用OE作半径在圆周上依次截出四个点...
季阅是4475圆内接正五边形的尺规作法
赵爬芸15244169871 ______ 圆内接正五边形的尺规作法 ①以O为圆心,定长R为半径画圆,并作互相垂直的直径MN和AP. ②平分半径ON,得OK=KN. ③以点K为圆心,KA为半径画弧与OM交于点H, AH即为正五边形的边长. ④以AH为弦长,在圆周上截得A,B,C,D,E各点,顺次连接这些点即得正五边形. ①以O为圆心,定长R为半径画圆,并作互相垂直的直径MN和AP. ②平分半径ON,得OK=KN. ③以点K为圆心,KA为半径画弧与OM交于点H, AH即为正五边形的边长. ④以AH为弦长,在圆周上截得A,B,C,D,E各点,顺次连接这些点即得正五边形.dfhj
季阅是4475在一个圆内怎样做出正五边形
赵爬芸15244169871 ______ 圆内接正五边形的画法如下: ①以O为圆心,定长R为半径画圆,并作互相垂直的直径MN和 AP. ② 平分半径ON,得OK=KN. ③以 K为圆心,KA为半径画弧与 OM交于 H, AH即为正五边形的边长. ④以AH为弦长,在圆周上截得A,B,C,D,E各点,顺次连接这些点即得正五边形. 这种画法得到的是标准正五边形
季阅是4475圆内接正五边形的画法证明 -
赵爬芸15244169871 ______ 虽然这个作法是初中可能就会给出,但是到高中时才能解释的.如果楼主是初中生的话,不需要知道为什么的,考试也不会考这么难的(除非竞赛).当然初中学生也能做...可以说这是个计算技巧问题. R为半径圆内接正五边形的边长没问...
季阅是4475尺规作图如何画圆内接正五边形怎么画 -
赵爬芸15244169871 ______ 画一个圆,然后做一条直径AB用圆规作起垂线,交于X点,用圆规取XB中点M连接CM以其为半径画弧交AB于N点连接NC以C为圆心CN为半径画弧交园O于K点接着仍以CN为半径K为圆心.以此类推
季阅是4475如何画圆内接五边形 -
赵爬芸15244169871 ______ [正五边形的画法] (1)已知边长作正五边形的近似画法如下: ①作线段AB等于定长l,并分别以A,B为圆心,已知长l为半径画弧与AB的中垂线交于K. ③以 C为圆心,已知边长 AB为半径画弧,分别与前两弧相交于M,N. ④顺次连接A,B,N,C,M各点...