WO2022218395A1 - 一种初中几何模板 - Google Patents

一种初中几何模板 Download PDF

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WO2022218395A1
WO2022218395A1 PCT/CN2022/086974 CN2022086974W WO2022218395A1 WO 2022218395 A1 WO2022218395 A1 WO 2022218395A1 CN 2022086974 W CN2022086974 W CN 2022086974W WO 2022218395 A1 WO2022218395 A1 WO 2022218395A1
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circle
hypotenuse
center
arc
radius
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PCT/CN2022/086974
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French (fr)
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姚颖旦
姚汉桢
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青岛智立亘生工程技术事务所
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
    • B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
    • B43L13/00—Drawing instruments, or writing or drawing appliances or accessories not otherwise provided for
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
    • B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
    • B43L5/00—Drawing boards
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
    • B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
    • B43L9/00—Circular curve-drawing or like instruments

Definitions

  • the invention relates to a junior high school geometric template, which specifically belongs to the technical field of surveying and mapping tools.
  • a conventional tool kit for drawing junior high school geometry includes: ruler, right-angled triangle (30°, 45°), protractor, and compass.
  • Architectural drafting templates group legends of common scales engraved on a slab.
  • mathematical templates that engrave commonly used geometric figures or function curves on the plate.
  • the drawing area of the traditional kit is limited to the inner and outer contour lines of the tool.
  • a single piece has a single function and needs to be used in combination, and the tools are scattered and easy to lose; Too many holes too large make the template large and fragile.
  • Geometry often derives the characteristics of general graphics from the characteristics of special graphics. For example, the basis of the circumcircle of a triangle is the vertical bisector of the line segment. Therefore, the special graphics with obvious characteristics is the core of geometry.
  • Geometry in junior high school starts from points, lines and angles, and the main figures involved are triangles, quadrilaterals and circles. Special triangles include: equilateral triangle, isosceles triangle, right triangle (especially 30° right triangle, 45° right triangle) and so on.
  • Special quadrilaterals include: square, rectangle, rhombus, parallelogram, trapezoid (especially right-angled trapezoid, isosceles trapezoid) and the like.
  • a circle includes arcs, chords, and angles (central angle, circumferential angle).
  • Special relations include: the shape of triangles and triangles (congruent, similar), the positions of circles and circles (inscribed, circumscribed, concentric), and the positions of triangles and circles (circumscribed, inscribed), etc.
  • the straightedge and the semicircular protractor (called the circles where the outer and inner arcs of the semicircle are located are arc A and arc B) enclose a semicircular area, and arc B and one long edge of the ruler form the outline of the semicircular area , the only diameter of the semicircle and the radius perpendicular to it form a Cartesian coordinate system.
  • the semicircle area take the diameter of the semicircle as the hypotenuse (the center of the circle is the midpoint of the hypotenuse), and make an inscribed 30° right triangle (the vertex of the right angle is located at 30° or 150° of the protractor); High and parallel to the median line of the three sides, and extend the two median lines parallel to the right-angled sides to intersect with the semicircle.
  • the semicircular protractor is used to mark angles and tick marks as usual.
  • the ruler takes the center of the semicircle as the origin, and marks the numbers in the form of a number axis. Cut the Leroy triangle and circle E along the edges, and the inner contour lines of the remaining holes are used for drawing, and the cut plates are used for comparison and experimentation.
  • Two points define a line segment; two points also define a circle.
  • the corresponding form of "point" on the template is the positioning hole:
  • Cartesian coordinate system Set bit holes at integer positions on the vertical and horizontal axes.
  • Protractor set holes at arc B corresponding to special angles (0 or 180°, 30 or 150°, 45 or 135°, 60 or 120°, 90°); If the lower hole is too close and the material strength is not enough, it is not necessary to set the position hole there; for the same reason, a certain distance should be maintained between the inner and outer arcs (arcs A and B) of the semicircle of the protractor.
  • a hole is set at the intersection with arc B; a hole is set at the center of each circle or arc.
  • the present invention integrates all the functions of a ruler, a triangular plate, a protractor and a part of a compass (the template can only draw an arc with the contour line or the positioning hole spacing as the radius, otherwise , the template cannot replace the compass with adjustable radius, such as making equal angles; if the drawing is not limited to the ruler, the template can be used to make equal angles with a protractor); the integrated pattern itself also contains important geometric relationships, which is helpful for the knowledge study.
  • 1-Arc B 2-diameter of the base of the semicircle area, 3-radius perpendicular to the diameter of the base, 4-30° right triangle, 5-midline of the hypotenuse, 6-height of the hypotenuse, 7- Corresponding to the median line of the hypotenuse, 8-corresponding to the median line and extension line of the long right-angle side, 9-corresponding to the median line and extension line of the short right-angle side, 10-circle C, 11-circle D, 12-Lello Triangle, 13-circle E, 14-circle F, 15-arc G;
  • Figure 5 An example of the relationship between a triangle and a circle
  • the ruler is 1x10cm (the measuring range of the ruler is 8cm, and the distance between the two ends is 1cm), the diameter of the semicircular arc A of the protractor is 10cm, and the diameter of the arc B is 8cm (then the distance between the two arcs is 1cm; the diameter of the circle E is 2cm, and the diameter of the concentric circles is 1cm; the diameter of the arc G and the arc on one side of the Leroy triangle are both 4cm; the diameter of the circle C is The diameter of circle D is ), the short side of the ruler is tangent to the outer ring of the protractor, enclosing a semicircular area with a diameter of 8cm, and an integrated pattern is connected inside the area.
  • the marking of ruler and protractor, the cutting of Leroy triangle and tangent circle, and the setting of positioning holes are as described above.
  • This template integrates the functions of ruler, triangular plate, protractor and part of compasses. It can be used directly, including but not limited to: (1) number axis and rectangular coordinate system; (2) special triangles: equilateral triangle, isosceles triangle, 30° and 45° right-angled triangle; (3) Special quadrilateral: square, rhombus, rectangle, parallelogram, isosceles trapezoid, right-angled trapezoid; (4) Circle: any two positioning holes can be made into a circle; (5) Leroy triangle; (6) ) The two line segments are parallel or perpendicular; (7) The triangles are similar or congruent; (8) The straight line and the circle (tangent); (9) The triangle and the circle: the inscribed circle of the large and small equilateral triangle (circle C and circle D, circle C Equal to the circumcircle of a small equilateral triangle), a 30° right triangle is inscribed in arc B; (10) Circle and circle: circle C and circle D intersect and pass through the center

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  • Drawing Aids And Blackboards (AREA)

Abstract

一种初中几何模板，其外周由半圆环量角器与直尺连接而成，内部围成一个半圆区域，在半圆区域嵌入有集成图案，按集成图案设置有定位孔或轮廓线，在作为半圆直径的直尺内侧，半圆圆心标注为原点，两边整数刻度线处标注为正负整数坐标。这种几何模板通过增加集成图案和定位孔-轮廓线体系，融合了直尺、三角板、量角器的全部和圆规的部分功能，集成图案本身包含了重要的几何关系，有助于相关知识的学习。

Description

一种初中几何模板 【技术领域】
本发明是一种初中几何模板，具体属于测绘工具技术领域。
【背景技术】
绘制初中几何图形的常规工具套件包括：直尺、直角三角板(30°、45°)、量角器和圆规。建筑制图模板将常用比例的图例分组镂刻在平板上。也有数学模板将常用的几何图形或函数曲线镂刻在平板上。
【发明内容】
传统套件的作图区局限于工具的内、外轮廓线，单件功能单一，需要组合使用，工具零散易丢失；镂刻模板的作图区扩展到材料内部，但图形简单罗列，缺少关联，开洞太多太大使模板变得大而脆弱。几何往往由特殊图形的特性推衍一般图形的特性，例如三角形外接圆的基础是线段的垂直平分线，所以，特性明显的特殊图形是几何的核心。初中几何由点、线、角出发，主要涉及的图形有三角形、四边形和圆。特殊三角形包括：正三角形、等腰三角形、直角三角形(尤其是30°直角三角形、45°直角三角形)等。特殊四边形包括：正方形、矩形、菱形、平行四边形、梯形(尤其是直角梯形、等腰梯形)等。圆包括弧、弦、角(圆心角、圆周角)。特殊关系包括：三角形与三角形的形状(全等、相似)、圆与圆的位置(内切、外切、同心)、三角形与圆的位置(外接、内切)等。
一、集成图案
直尺与半圆环形量角器(称半圆环的外、内弧所在圆为圆弧A和圆弧B)围成一个半圆区域，圆弧B及直尺的一侧长边缘构成半圆区域的轮廓线，该半圆唯一的直径和与之垂直的半径构成直角坐标系。
在半圆区域内，以半圆直径为斜边(圆心为斜边中点)，做内接30°直角三角形(直角顶点位于量角器30°或150°处)；在此三角形中做斜边的中线和高、平行于三边的中位线，延长两条平行于直角边的中位线至与半圆相交。
以前述线段的交点和交点间线段为基础作圆或圆弧：以平行于长直角边的中位线与高的交点为圆心，该圆心与高的垂足连线为半径作圆C；以圆C与高的非垂足交点为圆心，以该圆心与平行于斜边的中位线与高的交点的连线为半径作圆D；分别以直角顶点和两直角边中点为圆心，短直角边的一半为半径画弧，三段弧形成莱洛三角形；以平行于短直角边的中位线的延长线为直径作圆E；以圆E的半径为直径作其同心圆，圆F；以斜边中点为圆心，平行于短直角边的中位线为半径画半圆弧，圆弧G，与斜边交于两点。
二、定位孔、轮廓线及标注
半圆环形量角器如常标注角度及刻度线。直尺以半圆圆心为原点，按数轴形式标注数字。将莱洛三角形和圆E沿边缘裁切下来，所留孔洞的内轮廓线用于绘图，所裁板片用于对比和实验。
两点确定一条线段；两点也确定一个圆。“点”在模板上的对 应形式是定位孔：
(1)直角坐标系：在纵横数轴上的整数位置设定位孔。
(2)量角器：在圆弧B对应特殊角度(0或180°、30或150°、45或135°、60或120°、90°)处设孔；若因距离莱洛三角形及圆E留下的孔洞过近且材料强度不够，可不在该处设定位孔；同样原因，量角器半圆环的内外弧(圆弧A与B)间要保持一定的间距。
(3)30°直角三角形：在各顶点、各边中点、斜边高的垂足、平行于斜边的中位线与斜边中线的交点、平行于直角边的中位线的延长线与圆弧B的交点处设孔；各圆或圆弧的圆心处设孔。
当半圆直径的长度是直尺单位长度的四倍时，上述定位孔会有最多的重合，并使各圆或圆弧的直径数值更简单。运用外轮廓线(直尺和量角器)和内轮廓线(莱洛三角形和圆E)以及不同组合的定位孔可以绘制需要的不同图形。
有益效果：通过增加集成图案和定位孔-轮廓线体系，本发明融合了直尺、三角板、量角器的全部和圆规的部分功能(模板只能以轮廓线或以定位孔间距为半径画弧，否则，模板无法替代半径可调的圆规，例如做相等角；若作图不限于尺规，模板可以用量角器来做相等角)；集成图案本身也包含了重要的几何关系，有助于相关知识的学习。
【附图说明】
图1.集成图案
说明：1-圆弧B，2-半圆区域的底边直径，3-与底边直径垂直的半径， 4-30°直角三角形，5-斜边的中线，6-斜边的高，7-对应斜边的中位线，8-对应长直角边的中位线及延长线，9-对应短直角边的中位线及延长线，10-圆C，11-圆D，12-莱洛三角形，13-圆E，14-圆F，15-圆弧G；
图2.定位孔、轮廓线、标注(粗线为轮廓线，圆点为定位孔)；
图3.特殊三角形作图示例(以粗线连接成特殊图形)；
图4.特殊四边形作图示例(以粗线连接成特殊图形)；
图5.三角形与圆的关系示例；
图6.圆与圆的关系示例。
【具体实施方式】
为了使本发明的目的、方案及优点更加清楚明白，以下结合附图和实施例对发明做进一步详细说明。应当理解，此处所描述的具体实施例仅用于解释而不是限定发明。
以公制厘米(cm)为长度单位。直尺为1x10cm(直尺量程8cm，距离两端各1cm)，量角器半圆环圆弧A直径10cm，圆弧B直径8cm(则两弧间距1cm；圆E直径为2cm，其同心圆直径为1cm；圆弧G和莱洛三角形一边的圆弧的直径皆为4cm；圆C的直径是
Figure PCTCN2022086974-appb-000001
圆D直径是
Figure PCTCN2022086974-appb-000002
)，直尺短边与量角器外环相切，围成直径为8cm的半圆形区域，在区域内接集成图案。直尺及量角器标注、莱洛三角形与相切圆的裁割、定位孔的设置如前述。
此模板融合了直尺、三角板、量角器和部分圆规的功能，可以直接做的包括但不限于：(1)数轴及直角坐标系；(2)特殊三角形：正 三角形，等腰三角形，30°及45°直角三角形；(3)特殊四边形：正方形、菱形、矩形、平行四边形、等腰梯形、直角梯形；(4)圆：任意两个定位孔可做圆；(5)莱洛三角形；(6)两线段平行或垂直；(7)三角形相似或全等；(8)直线与圆(相切)；(9)三角形与圆：大小正三角形的内切圆(圆C和圆D，圆C与小正三角形的外接圆相等)、30°直角三角形内接于圆弧B；(10)圆与圆：圆C和圆D相交且过圆D圆心，圆E与圆弧B内切、与圆弧G外切、与圆F同心，圆弧G与B、A同心，圆弧G与莱洛三角形底边弧相切。

Claims (1)

  1. 一种初中几何模板，其外周由半圆环量角器与直尺连接而成，内部围成一个半圆区域，其特征是:
    在半圆区域嵌入集成图案：该半圆圆弧B(1)的唯一直径(2)和与之垂直的半径(3)构成直角坐标系；以半圆直径为斜边做内接30°直角三角形(4)，并作斜边的中线(5)、高(6)和中位线(7)，作两条直角边的中位线(8-9)并延长与圆弧B相交；以平行于长直角边的中位线与斜边高的交点为圆心，该圆心与斜边高的垂足连线为半径作圆C(10)；以圆C与斜边高的非垂足交点为圆心，以该圆心和斜边中位线与高的交点的连线为半径作圆D(11)；分别以30°直角三角形直角顶点、短直角边中点和斜边中线中点为圆心，短直角边的一半为半径画弧，三段弧形成莱洛三角形(12)；以短直角边中位线延长线与长直角边和圆弧B的交点连线为直径作圆E(13)；以圆E的半径为直径作其同心圆F(14)；以斜边中点为圆心，平行于短直角边的中位线为半径画半圆弧G(15)，交斜边于两点；
    按前述集成图案设置定位孔或轮廓线：在坐标轴的整数位设定位孔；在前述各圆或圆弧的圆心设定位孔；在两直角边、斜边及斜边中线的中点设定位孔；在斜边高的垂足设定位孔；在量角器内环圆弧B上对应特殊角0°、30°、45°、60°、90°、120°、135°、150°、180°处设定位孔；裁切莱洛三角形和圆E作内轮廓线；
    在作为半圆直径的直尺内侧，以圆弧B圆心为原点标注0，两边整数刻度线处标注正负整数坐标。
PCT/CN2022/086974 2021-04-16 2022-04-15 一种初中几何模板 WO2022218395A1 (zh)

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CN216184084U (zh) * 2021-04-16 2022-04-05 青岛智立亘生工程技术事务所(有限合伙) 一种初中几何模板
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Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN87207633U (zh) * 1987-05-06 1988-11-02 王京玗 万能三角规板
CN2267474Y (zh) * 1996-01-12 1997-11-12 周锷 多功能数学算尺
CN2535245Y (zh) * 2001-04-23 2003-02-12 李延龙 快速量画绘图尺
CN201214348Y (zh) * 2008-07-10 2009-04-01 凌吟文 简便多用三角板
CN201456787U (zh) * 2009-07-21 2010-05-12 朔州市朔城区第一中学校 多功能量角器
US20160047650A1 (en) * 2014-08-15 2016-02-18 Edgeline Holdings, LLC Angular Measurement Tool
CN206124558U (zh) * 2016-08-05 2017-04-26 李昭玥 一种多功能量角器
CN209320554U (zh) * 2018-12-29 2019-08-30 辽东学院 多功能画规
CN216184084U (zh) * 2021-04-16 2022-04-05 青岛智立亘生工程技术事务所(有限合伙) 一种初中几何模板

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN87207633U (zh) * 1987-05-06 1988-11-02 王京玗 万能三角规板
CN2267474Y (zh) * 1996-01-12 1997-11-12 周锷 多功能数学算尺
CN2535245Y (zh) * 2001-04-23 2003-02-12 李延龙 快速量画绘图尺
CN201214348Y (zh) * 2008-07-10 2009-04-01 凌吟文 简便多用三角板
CN201456787U (zh) * 2009-07-21 2010-05-12 朔州市朔城区第一中学校 多功能量角器
US20160047650A1 (en) * 2014-08-15 2016-02-18 Edgeline Holdings, LLC Angular Measurement Tool
CN206124558U (zh) * 2016-08-05 2017-04-26 李昭玥 一种多功能量角器
CN209320554U (zh) * 2018-12-29 2019-08-30 辽东学院 多功能画规
CN216184084U (zh) * 2021-04-16 2022-04-05 青岛智立亘生工程技术事务所(有限合伙) 一种初中几何模板

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