TOEFL READING 1993/10(3)
Marjorie Rice was an unlikely candidate for the role of mathematical
innovator. She had no formal education in mathematics save a single course
required for graduation from high school in 1939. Nonetheless, in 1975 she took
up a problem that professional mathematicians had twice left for dead , and
showed how much life as in it still.
The problem was tessellation , or tiling of the plane , involves taking
a single closed figure a triangle, for example, or a rectangle and fitting it
together with copies of itself so that aplane is covered without any gaps or
overlap. A region of this plane would look rather like a jigsaw puzzle whose
pieces are all identical. Rice worked primarily with polygons, which consist
only of straight lines. More specifically, she worked with convex polygons , in
which the line joining any two points on the polygon lies entirely within the
polygon itself or on one of its edges(A five-pointed star, for example, does not
qualify as a convex polygon.)
By the time Rice took up tiling, its basic properties had been
established. Obviously, any square can tile the plane, as many kitchen floors
have demonstrated. Equilateral triangles are also afairly clear-cut case. There
is one other regular polygon(a polygon whose angles, and sides, are equal) that
can tile the plane: the hexagon . This fact was established by the ancient
Greeks but had long before been exploited by honeybees in building their
honeycombs.
And what of irregular polygons? As it turns out any triangle or
quadrilateral , no matter how devoid of regularity, will tile theplane. On the
other hand, no convex polygon with more than six sides can do so, and the three
classes of convex hexagons that can were uncovered by the end of the First World
War. So the only real question left by the time Marjorie Rice began her work was
which convex pentagons tile the plane.
重点单词：
unlikely : a. 不太可能的
candidate : n. 候选人,投考者
mathematical : a. 数学的,精确的
innovator : n. 改革者,刷新者
formal : a. 正式的,形式的,礼仪的;n. 正式的社交活动
be left for dead : 没有办法解决的难题
tessellation : n. 镶嵌装饰,棋盘形布置,镶嵌式铺装
tiling : n. 盖瓦,铺瓷砖,瓦类,花砖
plane : n. 平面,飞机,水准;a. 平的,平面的,平坦的;vt. 将...刨平,刨平;vi.
翱翔,乘飞机旅行,刨
involve : vt. 包括,使陷于,潜心于,包围
rectangle : n. 长方形,矩形
gap : 门隙,缝隙；空隙；火花隙；间距,范围,区间,间隔；裂缝,裂口,缺口；放电器;
使产生裂缝,豁开
overlap : n. 重叠,重复;vt. 重叠,重复;vi. 迭盖
region : n. 区域,地方,地区,范围,区,领域,层
jigsaw : n. 竖锯;vt. 用竖锯锯
piece : n. 块,片,篇,碎片,部分;vt. 修补,修理,结合;vi. 接头
identical : a. 同一的,恒等的,完全相同的
primarily : ad. 主要地,首先地,基本地
polygon : n. 多角形,多边形
straight : n. 直线,直;a. 直的,笔直的,正直的,直接的,整齐的,连续的;ad.
直接地,立即,不断地
convex : a. 中凸的,凸圆的,凸面的;n. 凸状,凸面体,凸透镜
entirely : ad. 完全,全然,一概
properties : 道具
establish : vt. 建立,确立,制定;vi. 移植生长
obvious : a. 明显的,明白的,显然的
demonstrate : vt. 示范,证明;vi. 示威
equilateral : n. 等边形;a. 等边的
clear-cut : a. 轮廓清晰的,明白的,清楚的
hexagon : n. 六角形,六边形
ancient : a. 远古的,旧的
exploit : n. 功绩,勋绩;vt. 开发,利用,开拓,剥削
honeybee : n. 蜜蜂
honeycomb : n. 蜂巢,蜂房,蜂窝;a. 蜂巢的;vt. 开多孔使成蜂巢状;vi.
满是洞孔
quadrilateral : a. 四边形,四边地,四角地
devoid : a. 全无的,缺乏的
uncovered : a. 无遮盖的,未戴帽子的,未保险的
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