1,1

On a four day walk travelling west then north from Llanwrthwl to Ponterwyd,%C A162672 (two kilometres north of Ysbyty Cynfyn on Ordnance Survey Landranger Map 147 - Elan Valley - 1:50000 series);

I noticed a similarity in the shapes of the Cambrian Mountains which are very old and eroded.

They generally tend towards hemispheres but where peaks and crags do occur, walkers avoid most of these.

I argue that a circular walk measured on a flat map should be multiplyied by the Welsh Walking Constant

to find the actual distance covered. Half of Pi multiplied by (n)mapkilometres accounts for the vertical

dimension of the hill shapes. Laterally we tend to zigzag on steep slopes and make all sorts of minor

changes to the mapped route and multiplying all by half Pi again reflects these deviations over long enough distances.

Problem:- What other constants exist for different topographies?

For example:- a straight line walk across sand dunes is about the length of a Bell Curve over its axis.

Note:- I used Google Earth to simulate a 'flight' along my route. Such a flight anywhere in this area

quickly shows the outlines of the hill shapes encountered.

Cf. A091476

Sequence in context: A142473 A132426 A072646 this_sequence A091476 A114431 A167689

Adjacent sequences: A162669 A162670 A162671 this_sequence A162673 A162674 A162675

cons,nonn

Marco Matosic (marcomatosic(AT)hotmail.com), Jul 10 2009