KoG 5–2000/01 Blaˇzenka Divjak: Notes on Taxicab Geometry ¡ ¢ ¤ ¦ ¤ ¤ ¨ © Review Accepted 15. 12. 2000. " # $ % ' # * , - / 0 2 3 5 7 8 : 8 ? @ B D 3 F B I K 8 ? N 8 @ P 3 7 3 Ö ? @ 8 ? × Ø B D 3 F B I Ù 8 ? N 8 @ P Ú < = < T U W U \ U Û T U Ñ Y Z [ [ Ü [ ^ _ ` a c _ d f h i k h n p a r _ r h s t _ r h i s t h h x y z a s | y a } f h i k h n p a r _ ^ } h n _ ` a c _ d f h i k h n p à a | i t h i Ý t i t Þ x c z a s h _ t f h i k h n p a h | ^ x r h f h i k h n p a r x r i | p a r h f i s a t _ p _ k _ n p _ i h p h p k _ t t a t y i | y a h | _ k k h z n h d } _ t s z x t f h t a t n p i k _ t t a t y i | y a h | _ k k h z n h d } _ t s z x t f h t _ i s n _ s _ s x c h s n } a | f h i k h n p à k i p h n } _ t à h _ p | _ f i ß t n } a | s i a z r _ _ z _ r h h p a i s h k _ p f a t _ z a _ c a r h a f i n i i _ d i p _ _ } x t s p h s à h _ p | n } h p h h p h n } h h p a i s | i Ý k _ p f a t _ z a _ n a i t _ z a a h p a i s h h z a y i f _ t a k _ t r _ a | a p i y h p a k r h t h § _ t _ | _ t s n } h h p a i s | i Ý f p h _ n a t n h p h | n _ t s a s h _ z a c _ n a i t i Ý | h k i h p i t _ c © a c a n _ | h y n _ p x i n p h d h a p a k r h t h n _ ` a c _ d n } a | f h i k h n p à ^ i s _ à n } h p h a | _ } i z h | h c n h p i Ý _ z a c _ f h i k h n p a r h « _ n i i | n i r a a | h p _ z i f _ n a i t _ t s a k z h k h t n _ n a i t i Ý n } h n _ ` a c _ d f h i k h n p à ^ } h p h _ p h | h h p _ z p h _ | i t | Ý i p n } a | ® p i n _ ` a c _ d f h i k h n p a r _ d z a | y _ r h h x y z a s | y i r f h i k h n p a r a a Á a p | n n } h n _ ` a c _ d f h i k h n p à a | | a k a z _ p n i Þ x c z a s h _ t f h i k z _ f _ t _ _ p _ x k a r h _ t r h i h | h p i k _ n p _ n a y _ i k h n p a c y a h n p à _ t s h _ | à n i x t s h p | n _ t s ß n c _ t d h i d | h p h s _ | | x c } | x | n _ x y i r h k n i c y h y i p h | i t s a p _ r x y p a _ t r a k _ x z a c _ x _ k h n p a c | à | n h k } h p h n } h i a t n | c i p p h | i t s n i n } h a t _ k a | z r h t i k f p _ s x f s r h x z a c h a s x | _ k i } i p a i t n _ z t i a h p n h p | h c n a i t | i Ý n } h | n p h h n | a t n } h a k _ f a t h s c a n à | n p h h n | p x t n a y _ z t i a t h k _ r h s t i | k r h p t a } x z a c _ i s _ n z h a t _ a n _ ` a i t z à } i p a i t n _ z z à _ t s h p n a c _ z z à ^ } h p h _ p h t i i t h _ à c _ d f h i k h n p a r _ ´ _ i n _ y _ i f i s t _ r h _ a x c _ _ t r h t _ | n p h h n | Á p i k n } h p h a i x | s h | c p a n a i t n } h t _ k h n _ ` a c _ d s i s a z i k | y i k | n x s a r x x i d z a y x h | h r _ | h k a t _ p | y a } p _ s i _ f h i k h n p à _ p a | h | ^ } h n _ ` a c _ d f h i k h n p à a | _ p i p a _ n h n i a s a z i k | y a } p _ s i _ y _ i | n i r h i a | _ t i x µ ¶ · a µ ¸ · s a | c x | | i x n s x p a t f n } h x t s h p f p _ s x _ n h | n x s à a t n } h Ý i p k i Ý § p x f i n _ ` a c _ d f h i k h n p a r _ _ t a k z r a _ r h _ a x c _ _ t r h a h | | _ à | | h k a t _ p i p y | _ t s s a z i k _ n } h | a | _ | a n a | s h | c p a d h s | _ | n _ t i a | n _ n h i p a r | y h f h i k h n p a r h i f x c © h r x r h i a a t µ ¶ · _ t s µ ¸ · | _ n a x i n p h d i k | a t n h n a c y i f p a | n x _ y i r a r h x h i § _ a s â h c i t s n } h n _ ` a c _ d f h i k h n p à a | a t n h p h | n a t f Ý i p n } h i p h n a a z d h p n _ z a a k h n p a c y a k p a | n x i k _ y i r a r h _ | z x _ t c _ z f h i k h n p à | n x s à n i i ß n c _ t d h _ t _ z à h s d à | à t n } h n a c h i p f h § _ a s ½ a p y } i ¾ ¿ d _ i _ p a | n x _ i r _ | t r h t _ | x _ p i _ c } a t n p i s x c h s d à § _ a s a z d h p n i p d à k h n p a c _ a x i n p h d z r h t _ _ x i s h t r h n _ ` a c _ d f h i k h n p a r h x µ À · ® i | p i _ c } s h | c p a d h s d à h i p f h § _ a s ½ a p y } i ¾ h t n a i t h s n i r a a n p h c © a p a | n x x f h i k h n p a r a p h y i _ | n p _ y n t h _ z f h d p h a _ p i _ c } h | _ p h s h | c p a d h s _ t s s a | c x | | h s a t µ À · ^ } h p h a | n h i p a r h f p x _ y i r a | x x h z a Á h z a ` ´ z h a t a p n } x p  _ à z h à y i r a n } h n } a p s _ p i _ c } a t f h i k h n p à x | a t f _ d | n p _ c n f p i x | _ t s n p s a s _ | h f h i k h n p a r _ n p h d _ p i x c _ _ n a p h y i s r h z i _ t r _ f p i x n } h i p à ^ } a | _ p i _ c } _ | a t n p i s x c h s d à Á h z a ` ´ z h a t f p x h f a d _ t r _ t _ _ s _ t a | y x Ä _ s _ z r h s i y _ _ n c © h k i _ t s p n } x p  _ à z h à ^ } h à c z _ a k h s n } _ n f h i k h n p à } _ s n i d h t h y h i x c y h i h z a | a x n _ ` a c _ d f h i k h n p a r a | n x s a h s n } p i x f } _ c n a t f n } h f p i x i Ý k i n a i t | i t n } h f a h t ^ p h c © h p _ y n a c t _ r h p a r h s t i | n n _ ` a c _ d f h i k h n p a r h t r h a t _ | h n Á x p n } h p | i k h p i i | a n a i t | _ d i x n h z z a | h | a t n } h n _ ` a | a p i y _ p a k r h t r a i | n t _ | n _ p t h x p d _ t h p i d z h k h n p _ t | c _ d f h i k h n p à _ p h p i h s i p n _ z _ t a p _ t r _ f p _ s i _ a n s ¿ n a k p a k r h t _ f i i p a | h ^ } a p s n } h p _ c n a c _ z _ z x h i Ý n } h n _ ` a c _ d f h i k h n p à a | a n | t p x µ · a s h _ z a c _ n a i t a t x p d _ t n p _ t | i p n _ n a i t p i d z h k | c a n à \ Ç È É È t h h x y z a s | y _ f h i k h n p a r _ n _ ` a c _ d f h i k h n p a r _ Ê W Ë Ì Í Î Ì Ê W Î Ï z _ t t a t f _ t s | i i t ^ } a | _ z a c _ n a i t } _ | d h h t s h | c p a d h s a t µ · T Ñ Ò Ó Ó Ó ´ ¸ ¸ ¸ ¶ § Ð Ï Ô Õ Õ Ô Ô Õ \ t i t Þ x c z a s h _ t f h i k h n p à n _ ` a c _ d f h i k h n p Ã Ì ã ä å Í æ ç Ï 1 Introduction to taxicab geometry in space.