The time has come to issue a warning: this entire series of caches will be archived between May 1st and October 31st, 2022.
Caches in the Series
The series consists of: Archimedes (GC3TT8C), Bernoulli (GC3V9MW), Cayley (GC3W898), Descartes (GC3X0W7), Euclid (GC3XGN0), Fermat (GC413V5), Gauss (GC4219Z), Heron (GC4VGBX), Ingham (GC4WC72), Jarnik (GC4Z9PK), Kepler (GC4ZMRG), Lovelace (GC50BN6), Merryman (GC51D34) and Newton (GC5AJ04).
A Few Words about Archimedes, the Person
Archimedes (Greece; C3rd B.C.) is generally acknowledged to be the greatest mathematician among the ancients including Euclid in whose school he studied. He made contributions to number theory, algebra and analysis but is known best for his work in plane and solid geometry. Archimedes anticipated integral calculus and is thought to have developed calculus two millennia before Sir Isaac Newton. His achievements in physics include inventions such as the compound pulley and the hydraulic screw. He discovered formulae for the volume and surface area of a sphere, and may even have been first in proving the relationship between a circle's circumference and its area. Many consider that Archimedes was the greatest genius who ever lived.
Use a Pencil/Pen and Paper
Since we lack the technical ability to provide drawings as part of the cache descriptions, you will have to draw sketches - a 15 cm ruler is a good idea too - to illustrate the problems. And you can use a calculator if you wish . . . even a slide rule or an abacus if either would help!!
Background
You need to know the sum in degrees of the three angles in a triangle, the terms "opposite side" and "adjacent side" with respect to angles in a triangle and how to name a triangle and its parts.
The Questions
1. Given △ PQR, what might one call the side opposite ∡ PRQ? If PR, respond 1; if RQ, respond 2: if PQ, respond 3.
Your answer: A = _____.
2. Given △ STV, what might one call the side opposite ∡ VTS? If s, respond 4; if t, respond 5; if v, respond 6.
Your answer: B = _____.
3. Given △ WXY, what would one call the angle at vertex Y? If (angle) WXY, respond 7:_____; if XYW, respond 8:_____; if YWX, respond 9.
Your answer: C = _____.
4. Given that one angle of a triangle contains 78°, then what is the sum in degrees contained in the other two angles?
Your answer: DEF = _____ °.
5. If two angles in a triangle contain 45° and 88° respectively, then what is the size of the third angle?
Your answer: GH = _____ °.
The Co-ordinates
The cache can be found at N 44° jk.mnp’ and W 078° qr.stw’
There is no connection between the upper case letters above and the lower case letters here except as defined below.
The lower case letters can be found with a little arithmetic as follows using your answers above.
j = B - G: _____; k = D + H: _____; m = C + G - H: _____;
n = E + F: _____; p = A - F: _____; q = (C)(D) - A + E: _____;
r = (F)(G) - (B)(D): _____; s = D + F + (A)(E): _____;
t = (B)(G)(A) - (C)(H) + D: _____; w = C + H - (A)(B): _____.
The cache is at: N 44° __ __ . __ __ __ ‘ and W 078° __ __ . __ __ __’
BE SURE TO RECORD THE CORRECT CO-ORDINATES OF THE CACHE FOR USE IN LATER CACHES IN THIS SERIES!!
You can check your answers for this puzzle on GeoChecker.com.
Congratulations to uptownbrowns on their being FTF!