OpenMath Content Dictionary: units_imperial1

Canonical URL:

http://www.openmath.org/cd/units_imperial1.ocd

CD File:

units_imperial1.ocd

CD as XML Encoded OpenMath:

units_imperial1.omcd

Defines:

acre, bar, degree_Fahrenheit, foot, mile, miles_per_hr, miles_per_hr_sqrd, pint, pound_force, pound_mass, yard

Date:

2004-08-27

Version:

3 (Revision 2)

Review Date:

2017-12-31

Status:

experimental

---

     This document is distributed in the hope that it will be useful, 
     but WITHOUT ANY WARRANTY; without even the implied warranty of 
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

     The copyright holder grants you permission to redistribute this 
     document freely as a verbatim copy. Furthermore, the copyright
     holder permits you to develop any derived work from this document
     provided that the following conditions are met.
       a) The derived work acknowledges the fact that it is derived from
          this document, and maintains a prominent reference in the 
          work to the original source.
       b) The fact that the derived work is not the original OpenMath 
          document is stated prominently in the derived work.  Moreover if
          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
          chosen so that it cannot be confused with any works adopted by
          the OpenMath Society.  In particular, if there is a Content 
          Dictionary Group whose name is, for example, `math' containing
          Content Dictionaries named `math1', `math2' etc., then you should 
          not name a derived Content Dictionary `mathN' where N is an integer.
          However you are free to name it `private_mathN' or some such.  This
          is because the names `mathN' may be used by the OpenMath Society
          for future extensions.
       c) The derived work is distributed under terms that allow the
          compilation of derived works, but keep paragraphs a) and b)
          intact.  The simplest way to do this is to distribute the derived
          work under the OpenMath license, but this is not a requirement.
     If you have questions about this license please contact the OpenMath
     society at http://www.openmath.org.

  Author: OpenMath Consortium (James Davenport)
  SourceURL: https://github.com/OpenMath/CDs
            

This CD defines symbols to represent imperial standard measures.

---

foot

Description:

This symbol represents the measure of one foot. This is the standard imperial measure for distance.

Commented Mathematical property (CMP):

1 foot = 0.3048 metres

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="foot" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMF dec="0.3048"/>
      <OMS name="metre" cd="units_metric1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">foot</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">0.3048</cn>
   <csymbol cd="units_metric1">metre</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , foot) , times ( 0.3048 , metre) )

Popcorn

1 * units_imperial1.foot = 0.3048 * units_metric1.metre

Rendered Presentation MathML

$$1\mathrm{foot}=0.3048\mathrm{metre}$$

Signatures:

sts

---

[Next: yard] [Last: bar] [Top]

---

yard

Description:

This symbol represents the measure of one yard. This is a standard imperial measure for distance, defined in terms of the foot.

Commented Mathematical property (CMP):

1 yard = 3 feet

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="yard" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 3 </OMI>
      <OMS name="foot" cd="units_imperial1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">yard</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">3</cn>
   <csymbol cd="units_imperial1">foot</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , yard) , times ( 3 , foot) )

Popcorn

1 * units_imperial1.yard = 3 * units_imperial1.foot

Rendered Presentation MathML

$$1\mathrm{yard}=3\mathrm{foot}$$

Signatures:

sts

---

[Next: mile] [Previous: foot] [Top]

---

mile

Description:

This symbol represents the measure of one (land, or statute) mile. This is a standard imperial measure for distance, defined in terms of the foot.

Commented Mathematical property (CMP):

1 mile = 5280 feet

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="mile" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 5280 </OMI>
      <OMS name="foot" cd="units_imperial1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">mile</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">5280</cn>
   <csymbol cd="units_imperial1">foot</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , mile) , times ( 5280 , foot) )

Popcorn

1 * units_imperial1.mile = 5280 * units_imperial1.foot

Rendered Presentation MathML

$$1\mathrm{mile}=5280\mathrm{foot}$$

Signatures:

sts

---

[Next: acre] [Previous: yard] [Top]

---

acre

Description:

This symbol represents the measure of one acre. This is a standard imperial measure for area.

Commented Mathematical property (CMP):

1 acre = 4840 square yards

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="acre" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 4840 </OMI>
      <OMA>
        <OMS name="times" cd="arith1"/>
        <OMS name="yard" cd="units_imperial1"/>
        <OMS name="yard" cd="units_imperial1"/>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">acre</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">4840</cn>
   <apply><csymbol cd="arith1">times</csymbol>
    <csymbol cd="units_imperial1">yard</csymbol>
    <csymbol cd="units_imperial1">yard</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , acre) , times ( 4840 , times (yard, yard) ) )

Popcorn

1 * units_imperial1.acre = 4840 * units_imperial1.yard * units_imperial1.yard

Rendered Presentation MathML

$$1\mathrm{acre}=4840\mathrm{yard}\times \mathrm{yard}$$

Signatures:

sts

---

[Next: pint] [Previous: mile] [Top]

---

pint

Description:

This symbol represents the measure of one (imperial) pint. This is the standard imperial measure for volume. See units_us1 for the U.S. pint.

Commented Mathematical property (CMP):

1 pint = 0.568 litres

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="pint" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMF dec="0.568"/>
      <OMS name="litre" cd="units_metric1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">pint</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">0.568</cn>
   <csymbol cd="units_metric1">litre</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , pint) , times ( 0.568 , litre) )

Popcorn

1 * units_imperial1.pint = 0.568 * units_metric1.litre

Rendered Presentation MathML

$$1\mathrm{pint}=0.568\mathrm{litre}$$

Signatures:

sts

---

[Next: miles_per_hr] [Previous: acre] [Top]

---

miles_per_hr

Description:

This symbol represents the measure of one mile per hour. This is a standard imperial measure for speed.

Commented Mathematical property (CMP):

1 miles_per_hr = 1 mile in 1 hour

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="miles_per_hr" cd="units_imperial1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/> 
    <OMS name="mile" cd="units_imperial1"/> 
    <OMS name="hour" cd="units_time1"/> 
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_imperial1">miles_per_hr</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_imperial1">mile</csymbol>
   <csymbol cd="units_time1">hour</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (miles_per_hr, divide (mile, hour) )

Popcorn

units_imperial1.miles_per_hr = units_imperial1.mile / units_time1.hour

Rendered Presentation MathML

$$\mathrm{miles\_per\_hr}=\frac{\mathrm{mile}}{\mathrm{hour}}$$

Signatures:

sts

---

[Next: miles_per_hr_sqrd] [Previous: pint] [Top]

---

miles_per_hr_sqrd

Description:

This symbol represents the measure of one mile per hour squared. This is a standard imperial measure for acceleration.

Commented Mathematical property (CMP):

1 miles_per_hr_sqrd = 1 mile_per_hr (change) in 1 hour

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="miles_per_hr_sqrd" cd="units_imperial1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/> 
    <OMS name="miles_per_hr" cd="units_imperial1"/> 
    <OMS name="hour" cd="units_time1"/> 
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_imperial1">miles_per_hr_sqrd</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_imperial1">miles_per_hr</csymbol>
   <csymbol cd="units_time1">hour</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (miles_per_hr_sqrd, divide (miles_per_hr, hour) )

Popcorn

units_imperial1.miles_per_hr_sqrd = units_imperial1.miles_per_hr / units_time1.hour

Rendered Presentation MathML

$$\mathrm{miles\_per\_hr\_sqrd}=\frac{\mathrm{miles\_per\_hr}}{\mathrm{hour}}$$

Signatures:

sts

---

[Next: pound_mass] [Previous: miles_per_hr] [Top]

---

pound_mass

Description:

This symbol represents the measure of the mass which weighs one pound under the influence of standard gravity.

Commented Mathematical property (CMP):

1 pound = 0.45359237 kilograms

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="pound_mass" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMF dec="453.59"/>
      <OMS name="gramme" cd="units_metric1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">pound_mass</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">453.59</cn>
   <csymbol cd="units_metric1">gramme</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , pound_mass) , times ( 453.59 , gramme) )

Popcorn

1 * units_imperial1.pound_mass = 453.59 * units_metric1.gramme

Rendered Presentation MathML

$$1\mathrm{pound\_mass}=453.59\mathrm{gramme}$$

Signatures:

sts

---

[Next: pound_force] [Previous: miles_per_hr_sqrd] [Top]

---

pound_force

Description:

This symbol represents the measure of force of one pound.

Commented Mathematical property (CMP):

1 pound force = 4.44822 Newtons

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="pound_force" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMF dec="4.448"/>
      <OMS name="Newton" cd="units_metric1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">pound_force</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">4.448</cn>
   <csymbol cd="units_metric1">Newton</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , pound_force) , times ( 4.448 , Newton) )

Popcorn

1 * units_imperial1.pound_force = 4.448 * units_metric1.Newton

Rendered Presentation MathML

$$1\mathrm{pound\_force}=4.448\mathrm{Newton}$$

Signatures:

sts

---

[Next: degree_Fahrenheit] [Previous: pound_mass] [Top]

---

degree_Fahrenheit

Description:

This symbol represents the measure of one degree Fahrenheit. This is the standard imperial measure for temperature.

Commented Mathematical property (CMP):

1 degree Fahrenheit = 0.5556*(1-32) degrees Celsius

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="degree_Fahrenheit" cd="units_imperial1"/>
    </OMA>
    <OMA>
		  <OMS name="times" cd="arith1"/>
		  <OMF dec="0.5556"/>
			<OMA>
        <OMS name="minus" cd="arith1"/>
				<OMS name="degree_Celsius" cd="units_metric1"/>
  			<OMI> 32 </OMI>
			</OMA>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">degree_Fahrenheit</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">0.5556</cn>
   <apply><csymbol cd="arith1">minus</csymbol>
    <csymbol cd="units_metric1">degree_Celsius</csymbol>
    <cn type="integer">32</cn>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , degree_Fahrenheit) , times ( 0.5556 , minus (degree_Celsius, 32 ) ) )

Popcorn

1 * units_imperial1.degree_Fahrenheit = 0.5556 * (units_metric1.degree_Celsius - 32)

Rendered Presentation MathML

$$1\mathrm{degree\_Fahrenheit}=0.5556(\mathrm{degree\_Celsius}-32)$$

Signatures:

sts

---

[Next: bar] [Previous: pound_force] [Top]

---

bar

Description:

This symbol represents the measure of one bar. This is the standard imperial measure for pressure.

Commented Mathematical property (CMP):

1 bar = 100 000 Pascals

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 1 </OMI>
      <OMS name="bar" cd="units_imperial1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMI> 100000 </OMI>
      <OMS name="Pascal" cd="units_metric1"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_imperial1">bar</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">100000</cn>
   <csymbol cd="units_metric1">Pascal</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , bar) , times ( 100000 , Pascal) )

Popcorn

1 * units_imperial1.bar = 100000 * units_metric1.Pascal

Rendered Presentation MathML

$$1\mathrm{bar}=100000\mathrm{Pascal}$$

Signatures:

sts

---

[First: foot] [Previous: degree_Fahrenheit] [Top]