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Re: DesignerUnits: Gallons divided by km yields an area.

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  • Subject: [mg115780] Re: DesignerUnits: Gallons divided by km yields an area.
  • From: David Carraher <david_carraher at>
  • Date: Thu, 20 Jan 2011 06:32:23 -0500 (EST)


I'm impressed with the conception and functionality of DesignerUnits.

Here's a simple example. 

[Please excuse the formatting.  In Mathematica the formatting is much more 


Question 1: On average, how much (what volume of) gasoline does my car use 

to travel one meter if expends 4 gallons over 100 miles ?

There are more direct ways to solve this, but it's fun to divide gallons 

by km to get an area.

a. Four gallons divided by 100 miles gives an area.

In[1]:= (4¡Egallon)/(100¡Emile)

Out[2]= 9.40858*10^-8¡Esq£»m£»

Imagine this as the cross section of a pipe that runs alongside the car. 

The car consumes the gasoline corresponding to that contained in 

the pipe section it travels along.

Now multiply that cross-section by one meter to get a volume. 

That is how much gasoline is used along a one m stretch of road (assuming 

constant consumption).

In[3]:= ((4gallon)/(100mile) *1¡Em) 

Out[5]= 9.40858*10^-8¡Ecu£»m£»

Now convert back to gallons

In[6]:= ((4¡Egallon)/(100¡Emile) 1¡Em)/gallongallon

Out[6]= 0.0000248548£»gallon

In[7]:= Rationalize[%]Out[7]= 5/201168¡Egallon

Sure, you could have simply figured out how many meters are in a mile, but 

it wouldn't have been as much funn.

Here are some questions that can effortlessly be addressed:

"How many miles per hour does my hair grow?"

"How many Hiroshima atomic bombs would it take to raise the temperature of 

the Caribbean by 1 degree Celsius?

"How far does light travel in one nanosecond?"

It is particularly nice is to see the units displayed along the way, when 

computations are chained.



To: mathgroup at

Subject: [mg115780] [mg115585] Re: DesignerUnits 2011-01-08 for Mathematica 8, 7, 6

From: "Vincent N. Virgilio" <virgilio at>

Date: Sat, 15 Jan 2011 04:46:47 -0500 (EST)

The package includes a notebook for that. It produced a list of all

generated units by category. Forgot the name, but I, with diluted power of

concentration, found it somewhere in the install instructions.


On Fri, Jan 14, 2011 at 1:16 PM, DrMajorBob <btreat1 at> 


> The web pages are comprehensive if, for instance, you don't need a list 


> available units... unless it's there, but well hidden?


> Bobby


> On Fri, 14 Jan 2011 05:19:56 -0600, Vince Virgilio <blueschi at>

> wrote:


>  Well Bobby, it "worked for me", and perhaps completed sooner than

>> expected! (I went to sleep after launching it.)


>> A quick glance at this package's web pages showed them to be

>> sophisticated, comprehensive, and  convenient---a good mix. The

>> "backgrounder" page has a directness that is almost poetic.


>> Haven't used it yet, so we'll see how it plays out.


>> Vince



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