# Ptolemys' Ptools

## Star Fleet AcademyŠ "Trek-Ruler" :

### Go where no kid has gone before in geometry!

Using the Star Fleet Academy gameŠ, find the sizes of ships, space stations, stars, etc. by following the steps here. Use the "Scale Reference" below to get started or you can start with objects that others have scaled. In order to help us in our web page competition and pass your findings on to other game enthusiasts, PLEASE send your findings to us on our DATA RESPONSE FORM.

We will post your data (and first name) for others to use for reference points to collect more data.

### The Plan;

Do you have the software?

You need to have the Star Fleet Academy game to do this one, but it can work just as well on ANY 3D game. You just have to decide on a scale reference point and go from there.

 Scale Reference: Game Object "Real" size space station 743 km manual targeting sight always remains at 2 degrees for inner circle and 4 degrees for outer points

 Collecting the Data: (1) Place a piece of paper up to your computer's screen while the game is running with the station in view. Measure the height of the space station on your computer screen at a distance of about 4214 km (this works out to 10 degrees). The distance can be found in the upper left corner of your screen) Mark its height on the paper. (2) Scale your Trek-Ruler to your system; Get your TEXT RULER OR GRAPHIC RULER Transfer this measurement onto the Trek-Ruler, using one mark for the ZERO point on the scale and the other for the 10° mark. Mark the midway point between 0 and 10 for 5 degrees. Mark the midway point between 0 and 5 for 2.5 degrees. Mark double the length from 0 to 10 for 20 degrees. (3)Measure the angle (in degrees) of an object and record it on the data sheet (4)Look up the tangent ratio for that angle (5)Divide the object's known size by the tangent ratio to get the DISTANCE from the object. OR Multiply the object's known distance by the tangent ratio to get the SIZE of the object (width, height or diameter). Reporting back to Headquarters: (6) Record and submit the results on the data sheet.
 Tangent Angle Tangent Ratio 2.5° 0.0437 5° 0.0875 10° 0.1763 15° 0.2679 20° 0.3640