Assorted Brain Teasers by Kundan Pangtey - HTML preview

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TEASER - 14

LAT- X

The  latitude  reading  /  value  (Degrees)  on  the  summit  of  a mountain,  (say  Everest,  Chomolungma  or  Sagarmatha)  and  at its root is always same:

(a) True

(b) Falls

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THE EXPLANATION:

The earth's surface is divided by an imaginary set of grid lines, the longitude   and   the   parallels   of   latitude,   which   are   referred   as geographic  coordinate  system.  These  coordinates  appear  on  all standard maps and on some they may be the only way of locating and referencing a specific point.

(a)    Latitude lines

Latitude lines on the earth's surface are drawn connecting all points  equidistant  (parallel  of  latitude)  from  the  equator  and form  a  set  of  rings  around  the  globe.  The  latitude  value  is measured  from  the  equator,  with  positive  values  going  north and negative values going south. The equator is 0°latitude and the  North  Pole  and  South  Pole  are  90°N  and  90°S  latitudes, respectively.  The  length  of  one  degree  of  latitude  averages about 69 mile (110 km), it increases slightly from the equator to the poles as a result of the earth's polar flattening.

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(b)    Longitude lines:

Longitude  lines  are  a  set  of  north-south  rings  crossing  the equator  at  right  angle  and  converging  at  poles.  These  lines form   great   circles   and   always   divide   earth   into   two.   By international  agreement,  the  meridian  passing  through  the original site of the Royal Greenwich Observatory at Greenwich, England,  is  designated  the    prime  meridian,  and  all  points along it are at 0° longitude. All other points on the earth have longitudes ranging from 0°to 180°E or from 0°to 180°W.

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The Angle  ‘LAT-X’

The height of an elevation or depression on earth is measured along the  plumb  line.  A  plumb  line  is  defined,  as  a  line  from  which  if  a weight is suspended it is directed exactly toward the earth’s center of gravity.

The longitude plane and plumb line pass through the center of earth, and  fall  on  same  plane  and  do  not  cut  each  other.  On  the  other hand,  barring  equator,  the  latitude  plane  does  not  pass  through earth’s center hence both plumb line and latitude line do not fall on same plane and cut each other therefore are oblique to each other. The crux of the anomaly lies in the phenomenon of obliqueness of latitude plane with respect to plumb line.

The plumb line cuts latitude at an angle which increases from zero degree at equator, to 90 degrees at poles. This angle is referred to as “LAT-X” here.

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NORTHERN HEMISPHERE SHOWING ANGLE LAT-X

As  we  know,  contour  maps  are  generally  made  on  a  base  or reference plane, so that height or depth are calculated by counting contours up or down from the reference or base plane. While making a contour map, the location of  a point on earth surface, such as a mountain top, is transferred straight down onto a base plane along plumb  line  and  not  along  latitude  line.  Except  along  equator,  the Latitude lines and plumb lines (S - R line) are always oblique to each other, hence the location of S and R would not be at same point with respect to latitude values. However, on a contour map both S and R would be located exactly at same place, irrespective of height hence would have same latitude value.

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CROSS SECTION (X-Y) SHOWING S-R LINE (PLUMB LINE) OBLIQUELY CUTTING LATITUDE LINES

The  summit  (S)  and  root  (R)  of  a  mountain  can  be  likened  to  two floors of a building with S being first floor and R being ground floor. The  floors  are  linked  by  a  stair  case  which  is  parallel  to  latitude plane. Walking along the staircase from ground floor to first floor is like walking along a latitude plane. The staircase is always diagonal cutting   ground   and  1st    floors  at  different  points.  The   slope   of staircase would depend on angle ‘X’ and gap between two floors.

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LATITUDE LINES CUTTING A BUILDING DIAGONALLY

Therefore,  the  summit  (S),  like  first  floor,  shall  not  have  same latitude (staircase) as that at root (R) or ground floor, contrary to a contour map where both S and R are placed at same point.

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