4 2   km ▁( W GS 8 4 ▁polar ▁radius ▁" b "). ▁In ▁contrast ▁to ▁his ▁prede cess ors ▁who ▁measured ▁the ▁Earth ' s ▁circum ference ▁by ▁sight ing ▁the ▁Sun ▁simultaneously ▁from ▁two ▁different ▁locations , ▁Al - B ir uni ▁developed ▁a ▁new ▁method ▁of ▁using ▁trig on ometric ▁calculations ▁based ▁on ▁the ▁angle ▁between ▁a ▁plain ▁and ▁mountain ▁top ▁which ▁yield ed ▁more ▁accurate ▁measurements ▁of ▁the ▁Earth ' s ▁circum ference ▁and ▁made ▁it ▁possible ▁for ▁it ▁to ▁be ▁measured ▁by ▁a ▁single ▁person ▁from ▁a ▁single ▁location . ▁( cf . ▁) ▁Al - B ir uni ' s ▁method ' s ▁motiv ation ▁was ▁to ▁avoid ▁" walk ing ▁across ▁hot , ▁dust y ▁desert s " ▁and ▁the ▁idea ▁came ▁to ▁him ▁when ▁he ▁was ▁on ▁top ▁of ▁a ▁tall ▁mountain ▁in ▁India ▁( present ▁day ▁P ind ▁D ad an ▁Khan , ▁Pakistan ). ▁From ▁the ▁top ▁of ▁the ▁mountain , ▁he ▁sight ed ▁the ▁dip ▁angle ▁which , ▁along ▁with ▁the ▁mountain ' s ▁height ▁( which ▁he ▁calculated ▁before hand ), ▁he ▁applied ▁to ▁the ▁law ▁of ▁s ines ▁formula . ▁This ▁was ▁the ▁earliest ▁known ▁use ▁of ▁dip ▁angle ▁and ▁the ▁earliest ▁practical ▁use ▁of ▁the ▁law ▁of ▁s ines . ▁▁ ▁Ar ound ▁ 1 0 2 5 , ▁Al - B ir uni ▁was ▁the ▁first ▁to ▁describe ▁a ▁polar ▁equ i - az im uth al ▁equ id istant ▁projection ▁of ▁the ▁cel est ial ▁sphere