Sunday, August 15, 2021

Construction Pro 5: Geometry Algorithms

Construction Pro 5:  Geometry Algorithms


Before We Begin


Before we begin, some things to note:


1.  The [ Circ ] [ Circ ] sequence gives the area of a circle given by the denominator.  Area = (π * diameter^2) / 4 


2.  The [ Conv ] [ Rcl ] will clear the Construction Master 5's memory register.  So will [ Rcl ] [ Rcl ], the only difference is that the former sequence will not recall the memory's contents.


3.  The [ Rcl ] [ M+ ] sequence will recall the memory register's contents.


4.  The Construction Master 5 operates in Chain mode, like standard four-function calculators.  


5.  The algorithms presented today is one way to approach these calculation, most of them demonstrate the [ Circ ] [ Circ ] and memory features.   


Area:  Donut Driveway




Area = ((2D + I)^2 - I^2) * π/4


Key Sequence:


[ Conv ] [ Rcl ]

2 [ x ] D [ + ] I [ = ] [ Circ ] [ Circ ] [ M+ ]

I [ Circ ] [ Circ ] [ Conv ] ( M- )

[ Rcl ] [ M+ ]


Example:

D = 50 feet, I = 10 feet


[ Conv ] [ Rcl ]

2 [ x ] 50 [ Feet ] [ + ] 10 [ Feet ] [ = ] [ Circ ] [ Circ ] [ M+ ]

10 [ Feet ] [ Circ ] [ Circ ] [ Conv ] ( M- )

[ Rcl ] [ M+ ]


Result:  9,424.778 ft^2


Volume:  One-Hole Concrete Block




Note:  The border length (d) is equal around the entire block.


V = ( ( W + L ) * 2 * d - 4 * d^2 ) * t


Key Sequence:


[ Conv ] [ Rcl ]

W [ + ] L [ x ] 2 [ x ] d [ M+ ]

d [ Conv ] ( x^2 ) [ x ] 4 [ M- ]

[ Rcl ] [ M+ ] [ x ] t [ = ]


Example:

L = 12 in, W = 8 in, d = 1 in, t  10 in


[ Conv ] [ Rcl ]

8 [ Inch ] [ + ] 12 [ Inch ] [ x ] 2 [ x ] 1 [ Inch ] [ M+ ]

1 [ Inch ] [ Conv ] ( x^2 ) [ x ] 4 [ M- ]

[ Rcl ] [ M+ ] [ x ] 10 [ Inch ] [ = ]


Result:  360 in^3


Volume: Right Triangular Prism




V = D * H * B / 2 


Key Sequence:


D [ x ] H [ x ] B [ ÷ ] 2 [ = ]


Example:

D = 325 ft, H = 77 ft, B = 148 ft


325 [ Feet ] [ x ] 77 [ Feet ] [ x ] 148 [ Feet ] [ ÷ ] 2 [ = ]


Result:  1,851,850 ft^3 ≈ 68,587.04 yd^3


Volume:  Sphere Using the Circ Function





V = 4/3 * π * r^3 = π * d^3 / 6 = area_circle * d / 1.5

where area_circle = π * d^2 / 4


Key Sequence:


[ Conv ] [ Rcl ]

D [ M+ ] [ = ] [ Circ ] [ Circ ] [ x ] [ Rcl ] [ M+ ] [ ÷ ] 1.5 [ = ]


Note:  The first equals key "locks" in the value of D on to the register and allows it to be picked up with the Circ function without having to re-type it.  


Example:

D = 5 ft


[ Conv ] [ Rcl ]

5 [ Feet ] [ = ] [ M+ ] [ Circ ] [ Circ ] [ x ] [ Rcl ] [ M+ ] [ ÷ ] 1.5 [ = ]


Result: 65.44985 ft^3


Volume:  Column Using the Circ Function



V = π * D^2 * H / 4 = area_circle * H

where area_circle = π * d^2 / 4


Key Sequence:


D [ Circ ] [ Circ ] [ x ] H [ = ]


Example:

D = 2 ft 2 in, H = 1 ft 8 in


2 [ Feet ] 2 [ Inch ] [ Circ ] [ Circ ] [ x ] 1 [ Feet ] 8 [ Inch ] [ = ]


Result:  6.145013 ft^3


Commas added for readability.  


Eddie


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