CN106705775A - Irrational number intuitive measurement method and rule based on Pythagorean theorem - Google Patents
Irrational number intuitive measurement method and rule based on Pythagorean theorem Download PDFInfo
- Publication number
- CN106705775A CN106705775A CN201710048117.0A CN201710048117A CN106705775A CN 106705775 A CN106705775 A CN 106705775A CN 201710048117 A CN201710048117 A CN 201710048117A CN 106705775 A CN106705775 A CN 106705775A
- Authority
- CN
- China
- Prior art keywords
- measurement
- irrational number
- pythagorean theorem
- irrational
- directly perceived
- 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.)
- Pending
Links
- 238000000691 measurement method Methods 0.000 title abstract 4
- 238000005259 measurement Methods 0.000 claims abstract description 65
- 238000000034 method Methods 0.000 claims abstract description 24
- 239000000463 material Substances 0.000 claims description 12
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical compound [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 claims description 4
- 230000003068 static effect Effects 0.000 claims description 3
- 229910052742 iron Inorganic materials 0.000 claims description 2
- 229920003023 plastic Polymers 0.000 claims description 2
- 239000004033 plastic Substances 0.000 claims description 2
- 238000004519 manufacturing process Methods 0.000 abstract description 7
- 238000010586 diagram Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B3/00—Measuring instruments characterised by the use of mechanical techniques
- G01B3/002—Details
- G01B3/004—Scales; Graduations
- G01B3/006—Scales; Graduations having both coarse and fine graduation
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B1/00—Measuring instruments characterised by the selection of material therefor
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B3/00—Measuring instruments characterised by the use of mechanical techniques
- G01B3/02—Rulers with scales or marks for direct reading
- G01B3/04—Rulers with scales or marks for direct reading rigid
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Length-Measuring Instruments Using Mechanical Means (AREA)
Abstract
The invention discloses an irrational number intuitive measurement method and rule based on the Pythagorean theorem and belongs to the field of measurement. The irrational number intuitive measurement method based on the Pythagorean theorem, disclosed by the invention, comprises the specific steps: determining measurement precision and a measurement range of a real number rule according to actual measurement precision requirements; manufacturing the irrational number intuitive measurement rule based on the Pythagorean theorem; realizing irrational number length measurement of an object to be measured by utilizing the irrational number intuitive measurement rule, so as to solve actual problems. The invention further discloses the irrational number intuitive measurement rule based on the Pythagorean theorem; the irrational number intuitive measurement rule based on the Pythagorean theorem comprises a transverse axis for measuring an irrational number and a longitudinal axis for measuring a rooted integer irrational number. According to the irrational number intuitive measurement method and rule disclosed by the invention, intuitive measurement of a length of the irrational number is realized by reflecting a numerical relationship and a geometrical relationship between the irrational number and a rational number through a measurement process, and the measurement precision of the length of the irrational number can be adjusted according to measurement requirements, and application requirements of actual measurement are met; furthermore, the manufacturing is simple and the cost is low.
Description
Technical field
The invention belongs to fields of measurement, and in particular to a kind of irrational number based on Pythagorean theorem measuring method directly perceived and chi.
Background technology
There is much common survey tool, for example, measure ruler, the also angle square of measurement angle, triangle of length in life
Chi and engineer's scale etc., these scales are widely used in learning life so that people are during use to length, angle
Intuitively recognize etc. having.
Ruler is the instrument for gage length numerical value in mathematics, and the concept of number had both referred to real number actually in mathematics,
The definition of real number is to be referred to as real number by irrational number and rational.Our rulers used in study of living now are actually use
To measure the numerical value length of the scope of rational.Especially in junior middle school, learning stage high, learn in plane geometry, solid geometry
In substantial amounts of irrational number length along path angle value occurs.How intuitively impression measures surd length, and with have
The numerical relation and geometrical relationship that the length of reason number is contrasted so as to be better understood between irrational number and rational turn into real
Problem in the judgement of border.
The technology for solving the problem at present has：For irrational number with have several comparings, one, algebraically comparison method, it is first determined
Surd approximation quality, then compares the size of irrational number integer part and rational.If irrational number integer part is more than
Equal to rational, then irrational number numerical value is more than rational numerical value；If irrational number integer part is less than rational, irrational number number
Value is less than rational numerical value.2nd, number axis method, irrational number and rational are demarcated on same number axis, number axis by the left side and the right side according to
Secondary increase, knows between any two rational there is numerous irrational number again.Therefore on number axis demarcate the irrational number to be compared with
Rational, observes its distribution on number axis and judges rational and surd size, and irrational number is less than in left then irrational number
Rational, irrational number is more than rational in right then irrational number.
Therefore, in the prior art without irrational number measuring method directly perceived and measuring rule, it is badly in need of a kind of irrational number of invention directly perceived
Measuring method and chi.
The content of the invention
A kind of irrational number based on Pythagorean theorem measuring method directly perceived disclosed by the invention and chi, the technical problem to be solved
It is：The numerical relation and geometrical relationship reflected between irrational number and rational by metrics process are realized to surd length ground
Measurement directly perceived, can be adjusted to irrational number measurement of length precision according to measurement demand, meet actual survey engineering application demand.
The purpose of the present invention is achieved through the following technical solutions：
A kind of irrational number based on Pythagorean theorem measuring method directly perceived disclosed by the invention, specific steps include：
Step one, certainty of measurement and range that real number chi is determined according to Surveying Actual Precision requirement.
The irrational number measuring scale directly perceived of step 2, making based on Pythagorean theorem.
The irrational number based on Pythagorean theorem measuring scale directly perceived is included for measuring the transverse axis of rational and for measuring
Open the surd longitudinal axis of integer of radical sign.Transverse axis coordinate is according to certainty of measurement requirement with " 1 " for unit scale increases to aequum
Journey, the longitudinal axis is determined according to Pythagorean theorem, and the longitudinal axis isWherein Integer n is the scale of transverse axis.
Because described irrational number measuring scale directly perceived can also measure rational length, also known as real number chi.
Step 3, the irrational number length survey using the irrational number measuring scale realization directly perceived described in step 2 to testee
Amount.
According to tested length in kind, measurement of comparison is carried out with the transverse axis and the longitudinal axis and concrete graphic of real number chi respectively, and it is right
Measurement of comparison result is judged that transverse axis is used to measure rational, and the longitudinal axis is used to measure the integer irrational number for opening radical sign.During measurement
It is close to using real number chi on the figure for needing measurement, adjusts the position of real number chi, makes measured material object corresponding with real number chi
Scale maintains static reading after overlapping.
Step 4, using a kind of described irrational number based on Pythagorean theorem measuring method measurement irrational number length directly perceived,
Solving practical problems, for example：Irrational number linear measure longimetry teaching, solve engineer applied and daily using irrational number length measurement
Life practical problems.
Invention additionally discloses a kind of measuring scale directly perceived of the irrational number based on Pythagorean theorem, including for measuring the horizontal stroke of rational
Axle and open the surd longitudinal axis of integer of radical sign for measuring.The measurement of real number chi is determined according to the requirement of Practical Project certainty of measurement
Precision and range, transverse axis coordinate according to certainty of measurement requirement with " 1 " for needed for unit scale is increased to range, according to Pythagorean theorem
Determine the longitudinal axis, the longitudinal axis isWherein Integer n is the scale of transverse axis.
A kind of making material of described irrational number based on Pythagorean theorem measuring scale directly perceived often uses ruler material with the market
Material is identical.
Beneficial effect：
1st, a kind of irrational number based on Pythagorean theorem disclosed by the invention measuring method directly perceived and chi, anti-by metrics process
The numerical relation and geometrical relationship reflected between irrational number and rational are realized to the measurement directly perceived of surd length ground, to irrational number
Measurement of length precision can be adjusted according to measurement demand, meet actual survey engineering application demand.
2nd, a kind of irrational number based on Pythagorean theorem disclosed by the invention measuring method directly perceived and chi, making material and market
Upper conventional ruler material is identical, makes simple, low cost.
3rd, a kind of irrational number based on Pythagorean theorem disclosed by the invention measuring method directly perceived and chi, can realize survey directly perceived
Amount irrational number length, solving practical problems, for example：Irrational number linear measure longimetry is imparted knowledge to students, solved using irrational number length measurement
Engineer applied and daily life practical problems.
Brief description of the drawings：
Fig. 1 is real number chi principle assumption diagram；
Fig. 2 is integer irrational number measuring method schematic diagram in real number chi；
Fig. 3 is real number chi sample ruler principle exemplary plot；
Fig. 4 is real number chi sample ruler exemplary plot.
Specific embodiment
The present invention proposes intuitively measure the real number chi of irrational number and rational, can be complete by the use to real number chi
Intuitively measured for irrational number and rational into daily learning life and obtain its numerical value and geometrical relationship.
Develop simultaneously embodiment below in conjunction with the accompanying drawings, and the present invention will be described in detail.
A kind of measuring method directly perceived of irrational number based on Pythagorean theorem disclosed in the present embodiment, specific steps include：
Step one, certainty of measurement and range that real number chi is determined according to the requirement of Practical Project certainty of measurement.As shown in figure 1,
The requirement of Practical Project certainty of measurement is grade, and rational range is 23, and irrational number range isMillimeter is chosen as measurement
Precision, measuring length range isCentimetre.I.e.
B0B1=B1B2=B2B3=...=1cm (1)
The irrational number measuring scale directly perceived of step 2, making based on Pythagorean theorem, also known as real number chi, irrational number measuring scale directly perceived
Making material and in the market it is often identical with ruler material, preferably plastics or iron.
The irrational number based on Pythagorean theorem measuring scale directly perceived is included for measuring the transverse axis of rational and for measuring
Open the surd longitudinal axis of integer of radical sign.Transverse axis coordinate is according to certainty of measurement requirement with " 1 " for unit scale increases to aequum
Journey, the longitudinal axis is determined according to Pythagorean theorem, and the longitudinal axis isWherein Integer n is the scale of transverse axis.A0B0=1cm, A0B0⊥ l,(Pythagorean theorem) is with B1It is round dot, B1A0For radius is circular arc A0A1, A1B1⊥ l, thenTogether
SampleThe like.
As shown in Fig. 2 in right angled triangle △ AB0B1In, AB0=B0B1=1cm, according to Pythagorean theorem, two right-angle sides
Quadratic sum be equal to hypotenuse square, i.e. AB0 2+B0B1 2=AB1 2, soExtension B0B1To B2, make B1B2=B0B1
=1cm, crosses B1Point is B0B2Vertical line A1B1With B1It is the center of circle, AB1A length of radius is circular arc and A1B1Meet at point A1, i.e.,Connection A1B2.As shown in Figure 2.In right angled triangle △ A1B1B2In,B1B2=
1cm, according to Pythagorean theorem,SoAnd so on as shown in Figure 3.B0B1=B1B2
=B2B3=...=1cm, AB0=1cm,(irrational number also include as pi,
Trigonometric function etc. is not in real number chi measurement range), real number measurement sample ruler is as shown in Figure 3,4.
Step 3, the irrational number length survey using the irrational number measuring scale realization directly perceived described in step 2 to testee
Amount.
According to tested length in kind, measurement of comparison is carried out with the transverse axis and the longitudinal axis and concrete graphic of real number chi respectively, and it is right
Measurement of comparison result is judged that transverse axis is used to measure rational, and the longitudinal axis is used to measure the integer irrational number for opening radical sign.During measurement
It is close to using real number chi on the figure for needing measurement, adjusts the position of real number chi, makes measured material object corresponding with real number chi
Scale maintains static reading after overlapping.
Step 4, using a kind of described irrational number based on Pythagorean theorem measuring method measurement irrational number length directly perceived,
Solving practical problems, for example：Irrational number linear measure longimetry teaching, solve engineer applied and daily using irrational number length measurement
Life practical problems.
Engineer applied problem-instance is solved using irrational number length measurement：Field is manufactured in precision instrument, often essence
The parts requirement precision higher of close instrument, it will usually be accurate to after decimal point multidigit decimal place to ensure precision instrument just
Often use.General 0.05 millimeter to 0.01 millimeter of the certainty of measurement of common slide measure, and for precision instrument parts
During production, each parts production specification requirement, some parts requirement production specification is accurate to 4 to 5 millimeters after decimal point
Precision even more high, some now common graduated scales cannot meet accuracy requirement.But the fractional part for irrational number
It is the array of wireless circulating, first can be compared with the unreasonable number axis of real number chi when high accuracy parts are produced, finds out
Immediate irrational number can ensure certainty of measurement higher, specific implementation process i.e., precision instrument part to be measured with it is unreasonable
Number axis is adjacent to coincidence and compares, if instrument component to be measured coincide as qualified production specification with unreasonable number axis, it is possible to
The certainty of measurement of multidigit millimeter precision after guarantee decimal point, reaches the purpose of the parts production specification monitoring of precision instrument.
The present embodiment is also disclosed a kind of measuring scale directly perceived of the irrational number based on Pythagorean theorem, including for measuring rational
Transverse axis and open the surd longitudinal axis of integer of radical sign for measuring.The survey of real number chi is determined according to the requirement of Practical Project certainty of measurement
Accuracy of measurement and range, transverse axis coordinate according to certainty of measurement requirement with " 1 " for needed for unit scale is increased to range, according to hook stock determine
Reason determines the longitudinal axis, and the longitudinal axis isWherein Integer n is the scale of transverse axis.
In sum, presently preferred embodiments of the present invention is these are only, is not intended to limit the scope of the present invention.
All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., should be included in of the invention
Within protection domain.In sum, presently preferred embodiments of the present invention is these are only, protection of the invention is not intended to limit
Scope.All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., should be included in this hair
Within bright protection domain.
Claims (6)
1. a kind of irrational number based on Pythagorean theorem measuring method directly perceived, it is characterised in that：Comprise the following steps,
Step one, certainty of measurement and range that real number chi is determined according to Surveying Actual Precision requirement；
The irrational number measuring scale directly perceived of step 2, making based on Pythagorean theorem；
The irrational number based on Pythagorean theorem measuring scale directly perceived include for measure rational transverse axis and for measure open root
Number the surd longitudinal axis of integer；Transverse axis coordinate according to certainty of measurement requirement with " 1 " for needed for unit scale is increased to range, root
Determine the longitudinal axis according to Pythagorean theorem, the longitudinal axis isWherein Integer n is the scale of transverse axis；
Because described irrational number measuring scale directly perceived can also measure rational length, also known as real number chi.
Step 3, the irrational number linear measure longimetry using the irrational number measuring scale realization directly perceived described in step 2 to testee.
2. a kind of irrational number based on Pythagorean theorem measuring method directly perceived as claimed in claim 1, it is characterised in that：Also include
Step 4,
Step 4, using a kind of described irrational number based on Pythagorean theorem measuring method measurement irrational number length directly perceived, solve
Practical problem, for example：Irrational number linear measure longimetry is imparted knowledge to students, solves engineer applied and daily life using irrational number length measurement
Practical problems.
3. a kind of irrational number based on Pythagorean theorem measuring method directly perceived as claimed in claim 1 or 2, it is characterised in that：Step
Rapid three concrete methods of realizing is,
According to tested length in kind, measurement of comparison is carried out with the transverse axis and the longitudinal axis and concrete graphic of real number chi respectively, and to contrast
Measurement result is judged that transverse axis is used to measure rational, and the longitudinal axis is used to measure the integer irrational number for opening radical sign；Used during measurement
Real number chi is close on the figure for needing measurement, adjusts the position of real number chi, makes the measured corresponding scale with real number chi in kind
Reading is maintained static after coincidence.
4. a kind of irrational number based on Pythagorean theorem measuring scale directly perceived, it is characterised in that：Including the transverse axis for measuring rational
And the surd longitudinal axis of integer of radical sign is opened for measuring；The measurement essence of real number chi is determined according to the requirement of Practical Project certainty of measurement
Degree and range, transverse axis coordinate according to certainty of measurement requirement with " 1 " for needed for unit scale is increased to range, it is true according to Pythagorean theorem
Determine the longitudinal axis, the longitudinal axis isWherein Integer n is the scale of transverse axis.
5. a kind of irrational number based on Pythagorean theorem measuring scale directly perceived as claimed in claim 4, it is characterised in that：Described nothing
The making material of gage is often identical with ruler material with the market several times for reason.
6. a kind of irrational number based on Pythagorean theorem measuring scale directly perceived as claimed in claim 5, it is characterised in that：Described nothing
The making material for managing gage several times is plastics or iron.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710048117.0A CN106705775A (en) | 2017-01-20 | 2017-01-20 | Irrational number intuitive measurement method and rule based on Pythagorean theorem |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710048117.0A CN106705775A (en) | 2017-01-20 | 2017-01-20 | Irrational number intuitive measurement method and rule based on Pythagorean theorem |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN106705775A true CN106705775A (en) | 2017-05-24 |
Family
ID=58910129
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710048117.0A Pending CN106705775A (en) | 2017-01-20 | 2017-01-20 | Irrational number intuitive measurement method and rule based on Pythagorean theorem |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106705775A (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR1357325A (en) * | 1963-05-16 | 1964-04-03 | Micro Sine Entpr | Sinus angle enhancements |
| CN2323348Y (en) * | 1997-10-07 | 1999-06-09 | 齐乃强 | Multifunctional plotting ruler |
| US20070074413A1 (en) * | 2005-10-04 | 2007-04-05 | Neuroth Brad J | Digital speed square apparatus and method for using the same |
| CN201015068Y (en) * | 2006-12-15 | 2008-01-30 | 齐悦如 | Irrational number demonstrating ruler |
| CN101734060A (en) * | 2008-11-26 | 2010-06-16 | 曹俊晖 | Square root feet |
| CN205238950U (en) * | 2015-12-10 | 2016-05-18 | 郭子昂 | Irrational number approximate value ruler |
-
2017
- 2017-01-20 CN CN201710048117.0A patent/CN106705775A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR1357325A (en) * | 1963-05-16 | 1964-04-03 | Micro Sine Entpr | Sinus angle enhancements |
| CN2323348Y (en) * | 1997-10-07 | 1999-06-09 | 齐乃强 | Multifunctional plotting ruler |
| US20070074413A1 (en) * | 2005-10-04 | 2007-04-05 | Neuroth Brad J | Digital speed square apparatus and method for using the same |
| CN201015068Y (en) * | 2006-12-15 | 2008-01-30 | 齐悦如 | Irrational number demonstrating ruler |
| CN101734060A (en) * | 2008-11-26 | 2010-06-16 | 曹俊晖 | Square root feet |
| CN205238950U (en) * | 2015-12-10 | 2016-05-18 | 郭子昂 | Irrational number approximate value ruler |
Non-Patent Citations (1)
| Title |
|---|
| 宁挺: "勾股絮语(三)" * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN101876536B (en) | Three-dimensional color gradation comparison dynamic analysis method | |
| CN104391603A (en) | Method, device and system for calibrating touch screen | |
| CN206656765U (en) | A kind of combination type multifunction water leveling ruler | |
| Frolov et al. | The accuracy of area measurement by point counting techniques | |
| CN105466365B (en) | The method for obtaining radar corner reflector RCS precision | |
| CN204514216U (en) | A kind of slide calliper rule protractor | |
| CN201769555U (en) | Multifunctional mathematical ruler | |
| CN206683506U (en) | A kind of irrational number based on Pythagorean theorem measuring scale directly perceived | |
| CN106705775A (en) | Irrational number intuitive measurement method and rule based on Pythagorean theorem | |
| CN103837102A (en) | Sampling method for measuring surface roughness of circular optical plane | |
| CN104697423B (en) | The gauge and measuring method of counterbore angle | |
| CN107607080A (en) | A kind of prism-shaped cross-section of pipeline distortion measurement evaluation method | |
| CN102269581A (en) | Machining precision evaluation method of architectural component | |
| CN203995340U (en) | Set square with calipers angle measurement device | |
| CN106813563B (en) | Angle measuring device | |
| CN109631709B (en) | Measuring device for planar design convenient to carry | |
| CN103587302B (en) | Major-minor vernier scale | |
| CN201069347Y (en) | Cursor omnipotent combined angle ruler | |
| US20120003618A1 (en) | Geo-meter graph reader learning system | |
| CN206974320U (en) | Triangle mark plate shape dimension measurement slide calliper rule | |
| CN211373390U (en) | Double-pointer protractor | |
| CN206357876U (en) | A kind of multifunctional drawing ruler | |
| CN204404971U (en) | A kind of arc measuring instrument | |
| CN205940554U (en) | Measure appurtenance that hull was sheltered from a coordinate position | |
| CN104634294A (en) | Method for detecting and evaluating geometric error of grooved pulley of curved groove |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20170524 |