CN204632192U - A kind of equilateral triangle area and sum of series demonstrator - Google Patents
A kind of equilateral triangle area and sum of series demonstrator Download PDFInfo
- Publication number
- CN204632192U CN204632192U CN201520364392.XU CN201520364392U CN204632192U CN 204632192 U CN204632192 U CN 204632192U CN 201520364392 U CN201520364392 U CN 201520364392U CN 204632192 U CN204632192 U CN 204632192U
- Authority
- CN
- China
- Prior art keywords
- volume
- measuring cup
- individual unit
- scale mark
- equilateral triangle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Landscapes
- Details Of Rigid Or Semi-Rigid Containers (AREA)
Abstract
The utility model relates to education and instruction apparatus, a kind of equilateral triangle area and sum of series demonstrator form primarily of transparent cylinder container and one group of measuring cup, the length of side of described equilateral triangle is a unit, and described transparent cylinder container has scale mark, and described in Article 1, scale mark volume is from the bottom up
described in individual unit, Article 2, scale mark volume is
described in individual unit, Article 3, scale mark volume is
individual unit, by that analogy, topmost a described scale mark volume is
individual unit, the measuring cup number of described one group of measuring cup is many as far as possible, and first described measuring cup volume is
individual unit, second described measuring cup volume is
individual unit, the 3rd described measuring cup volume is
individual unit, by that analogy, the volume of described one group of measuring cup is corresponding with the scale mark of described transparent cylinder container.
Description
Technical field
The utility model relates to education and instruction apparatus, particularly a kind of equilateral triangle area and sum of series demonstrator, student can be made very intuitively to quantize geographical to separate infinite the specific equilateral triangle area sum i.e. geometric meaning of its sum of series.
Background technology
Student needs when learning higher mathematics to ask sum of series, such as: in the length of side be a equilateral triangle in, connect each limit mid point and do to connect equilateral triangle in one, so continue work and go down, calculate the area sum S of all these equilateral triangles, required be infinite series and:
obtaining result according to Geometric Sequence and convergent series and knowledge is:
said process can or can not be too abstract in Eyes of Students, if teaching aid demonstration intuitively can be had, have good effect, described a kind of equilateral triangle area and sum of series demonstrator can solve and understand infinite the specific equilateral triangle area sum i.e. problem of the geometric meaning of its sum of series quantitatively.
Utility model content
In order to enrich education and instruction apparatus, solve some apparent problem of sum of series in higher mathematics, the utility model provide a kind of equilateral triangle area and sum of series demonstrator, student can be made very intuitively to quantize geographical necessary condition (limit of progression general term equals zero when n levels off to infinity) of separating infinite specific equilateral triangle area sum and series convergence.
The scheme that the utility model adopts is:
Described a kind of equilateral triangle area and sum of series demonstrator form primarily of transparent cylinder container and one group of measuring cup, the length of side of described equilateral triangle is a unit, and described transparent cylinder container has scale mark, and described in Article 1, scale mark volume is from the bottom up
described in individual unit, Article 2, scale mark volume is
described in individual unit, Article 3, scale mark volume is
individual unit, by that analogy, topmost a described scale mark volume is
individual unit, the measuring cup number of described one group of measuring cup is many as far as possible, and first described measuring cup volume is
individual unit, second described measuring cup volume is
individual unit, the 3rd described measuring cup volume is
individual unit, by that analogy, the volume of described one group of measuring cup is corresponding with the scale mark of described transparent cylinder container.
The beneficial effects of the utility model are:
Described a kind of equilateral triangle area and sum of series demonstrator simple structure easily realize, student can be made very intuitively to quantize geographical to separate infinite the specific equilateral triangle area sum i.e. geometric meaning of its sum of series and the necessary condition of series convergence.
Accompanying drawing explanation
Further illustrate below in conjunction with figure of the present utility model:
Fig. 1 is described transparent cylinder container schematic diagram;
Fig. 2 is first described measuring cup schematic diagram;
Fig. 3 is second described measuring cup schematic diagram;
Fig. 4 is the 3rd described measuring cup schematic diagram.
In figure, 1. scale mark.
Embodiment
As Fig. 1 be as described in transparent cylinder container schematic diagram, described a kind of equilateral triangle area and sum of series demonstrator described in the length of side of equilateral triangle be a unit, described transparent cylinder container has scale mark (1), and described in Article 1, scale mark volume is from the bottom up
described in individual unit, Article 2, scale mark volume is
described in individual unit, Article 3, scale mark volume is
individual unit, by that analogy, topmost a described scale mark volume is
individual unit is required sum of series.
If Fig. 2 is that as described in first, measuring cup schematic diagram volume is
individual unit.
If Fig. 3 is that as described in second, measuring cup schematic diagram volume is
individual unit.
If Fig. 4 is that as described in the 3rd, measuring cup schematic diagram volume is
individual unit.
The volume of described one group of measuring cup is corresponding with the scale mark (1) of described transparent cylinder container, and the measuring cup number of described one group of measuring cup is many as far as possible.
During demonstration, first described one group of measuring cup is all filled water, successively by first described measuring cup, second described measuring cup, the 3rd described measuring cup ... in water all pour in described transparent cylinder container, can be observed visually liquid level from the bottom up scale mark described in scale mark, Article 3 described in scale mark, Article 2 described in Article 1 successively on move, until the described scale mark in the top, its total measurement (volume) is infinitely close to a constant, is required sum of series
Claims (1)
1. an equilateral triangle area and sum of series demonstrator, form primarily of transparent cylinder container and one group of measuring cup, the length of side of described equilateral triangle is a unit, it is characterized in that: described transparent cylinder container has scale mark (1), and described in Article 1, scale mark volume is from the bottom up
described in individual unit, Article 2, scale mark volume is
described in individual unit, Article 3, scale mark volume is
individual unit, by that analogy, topmost a described scale mark volume is
individual unit, the measuring cup number of described one group of measuring cup is many as far as possible, and first described measuring cup volume is
individual unit, second described measuring cup volume is
individual unit, the 3rd described measuring cup volume is
individual unit, by that analogy, the volume of described one group of measuring cup is corresponding with the scale mark (1) of described transparent cylinder container.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201520364392.XU CN204632192U (en) | 2015-05-25 | 2015-05-25 | A kind of equilateral triangle area and sum of series demonstrator |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201520364392.XU CN204632192U (en) | 2015-05-25 | 2015-05-25 | A kind of equilateral triangle area and sum of series demonstrator |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN204632192U true CN204632192U (en) | 2015-09-09 |
Family
ID=54051194
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201520364392.XU Expired - Fee Related CN204632192U (en) | 2015-05-25 | 2015-05-25 | A kind of equilateral triangle area and sum of series demonstrator |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN204632192U (en) |
-
2015
- 2015-05-25 CN CN201520364392.XU patent/CN204632192U/en not_active Expired - Fee Related
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN203746300U (en) | Demonstration apparatus for three-dimensional solid geometry teaching of mathematics course | |
| CN204463605U (en) | Archimedes principle quadruple inspection demonstrator | |
| CN204143712U (en) | A kind of buoyancy demonstrating device | |
| CN204632192U (en) | A kind of equilateral triangle area and sum of series demonstrator | |
| CN204632189U (en) | A kind of wooden stick length and sum of series demonstrator | |
| CN205068912U (en) | Mathematical education display unit of primary school utensil | |
| CN204537564U (en) | A kind of inclined plane demonstrating device for physics teaching | |
| CN203013071U (en) | Demonstrator for overweight and weightlessness | |
| CN204066536U (en) | Buoyancy produces demonstrating device | |
| CN204667711U (en) | A kind of exponential function is launched into power series demonstrator | |
| CN204667708U (en) | A kind of convergent series and demonstrator | |
| CN203026001U (en) | Addition-subtraction operation demonstrator for deaf-mute children | |
| CN206451425U (en) | A kind of teaching planar pattern demonstration device | |
| CN202771682U (en) | Exponential function rotating body volume definite integral demonstration instrument | |
| CN204596261U (en) | A kind of square is solved a problem demonstration teaching aid | |
| CN202331984U (en) | Demonstrator of common mathematical patterns | |
| CN205334823U (en) | Mathematic model show shelf of imparting knowledge to students | |
| CN204596260U (en) | Dovetail groove apparatus for demonstrating | |
| CN202563770U (en) | Archimedes law teaching demonstrator | |
| CN202443654U (en) | Ball volume verification demonstrator | |
| CN204695641U (en) | A kind of physics education resistive two force balancing demonstrator | |
| CN204143713U (en) | The all-round exploring instrument of buoyancy factor | |
| CN204332177U (en) | A kind of compression volute spring stiffness factor experimental provision | |
| CN202656722U (en) | Set square capable of being folded into regular triangular pyramid | |
| CN204720041U (en) | A kind of mathematics round platform demonstration teaching aid |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20150909 Termination date: 20160525 |