University of Houston math contests

07112019, 01:12 AM
(This post was last modified: 07112019 01:50 AM by telemachos.)
Post: #1




University of Houston math contests
Held each year, intended for high school students, they include calculator exams.
These HP calculators are now permitted (early on, only TI calculators were permitted): HP9G HP28 series HP38G HP39 series HP40 series HP48 series HP49 series HP50 series Exams going back to 2008 can be downloaded from here: <http://mathcontest.uh.edu/> Forum members may find this trove of problems amusing, trivial, or (in some cases) worthwhile education in the use of their HP calculator. (Not surprisingly, the HP50 has some distinct advantages over the other permitted models.) 

07112019, 03:30 PM
Post: #2




RE: University of Houston math contests
For example, I found this problem, from the 2019 exam, worthwhile:
A quadrilateral has its vertices (listed in clockwise order) as (–6.94, –1.2), (–5.16, 3.84), (3.4, 2.18), and (2.46, –6.72). Give the area of this quadrilateral. Surveyors among you may recognize this one. A short RPL program on the 50g solves it quickly. 

07112019, 08:26 PM
Post: #3




RE: University of Houston math contests  
07112019, 10:36 PM
Post: #4




RE: University of Houston math contests
(07112019 03:30 PM)telemachos Wrote: (–6.94, –1.2), (–5.16, 3.84), (3.4, 2.18), and (2.46, –6.72). Another way is to calculate angles θ between 2 diagonals: Slope m1 = (2.18 + 1.2) / (3.4 + 6.94) = 3.38 / 10.34 Slope m2 = (6.72  3.84) / (2.46 + 5.16) = 10.56 / 7.62 tan(θ) = (m1m2) / (1 + m1 m2) ≈ 3.13114 sin(θ) = tan(θ) / √(1 + tan(θ)²) ≈ 0.952598 area = ½ product of diagonals * sin(θ) ≈ ½ √(3.38² + 10.34²) * √(10.56² + 7.62²) * 0.952598 = 67.473 

07122019, 10:34 AM
(This post was last modified: 07122019 12:09 PM by Albert Chan.)
Post: #5




RE: University of Houston math contests
(07112019 08:26 PM)John Keith Wrote: It's already done for you. For quadrilateral, we could reduce ops with a more compact formula. Area = ½(x3x1)(y4y2)  (x4x2)(y3y1) This reduce Shoelace 9 multiply and 8 add/sub to just 3 multiply and 5 subtract. We could also use this formula for triangle area, by letting {x4,y4} = {x3,y3} Example, with XCas: area4(a,b,c,d) := 0.5*abs(det([ca,db])) area3(a,b,c) := area4(a,b,c,c) a,b,c,d := [6.94,1.2], [5.16, 3.84], [3.4,2.18], [2.46,6.72] area4(a,b,c,d) → 67.473 area3(a,b,c) + area3(a,c,d) → 23.0486 + 44.4244 = 67.473 

07122019, 04:41 PM
Post: #6




RE: University of Houston math contests
I think this makes the best use of the HP50g's capabilities:
Input: { [–6.94 –1.2] [–5.16 3.84] [3.4 2.18] [2.46 –6.72] } Program (56.5 bytes): << DUP HEAD + << CROSS >> DOSUBS ΣLIST ABS 2 / >> Output: 67.473 

07122019, 11:33 PM
(This post was last modified: 07122019 11:35 PM by RMollov.)
Post: #7




RE: University of Houston math contests
(07122019 04:41 PM)telemachos Wrote: I think this makes the best use of the HP50g's capabilities: ... and the one I've been using in my survey package for 20+ years on HP48G 

07132019, 01:15 PM
Post: #8




RE: University of Houston math contests
(07122019 04:41 PM)telemachos Wrote: I think this makes the best use of the HP50g's capabilities: Very nice program! I think it is the smallest HP48 compatible shoelace program yet. It can be made even shorter using the nulltag method from this thread, which shaves 9 bytes off the size, like so: Code:
I will also link my shoelace thread to this one. 

07132019, 03:57 PM
Post: #9




RE: University of Houston math contests
(07122019 04:41 PM)telemachos Wrote: ... Getting the data into that format could be an awkward exercise if attempting to enter it directly from the calculator's keyboard. It's very close, though, to the format that would exist if you used the builtin MatrixWriter to create it: Code: [[–6.94 –1.2] [–5.16 3.84] [3.4 2.18] [2.46 –6.72]] On both the 48GX and the 50g, the following two commands will convert a matrix created by the MatrixWriter to a "list of vectors" format compatible with the given shoelace programs in this thread: Code: →ROW →LIST I find the MatrixWriter to be convenient for this type of data entry (as well as maintenance). Judicious use of the various array commands (and AXL on the 50g) can often help to transform an array to a wide variety of useful formats. 

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