Repository: UIHistories Project: Mathematical Models Construction and Use of Mathematical Models (Fehr & Hildebrandt) [PAGE 9]

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2. Parallelogram: Join two sticks of ^ \^-*^^ / u n e a u a i l e n g t h by a single b o l t at their midS ^V*^-v^< /' p o i n t s • S t r e t c h an elastic tane around the . s N / edges, As the sticks are m o v e d in any p o s i *r. _ _ — tion the elastic b a n d always forms a p a r a l l e l o g r a m . 3. Diagonals: Join two u n e a u a i pairs of emial s t i c k s , a l t e r n a t e l y , by single b o l t s . F a s t e n elastic d i a g o n a l s * For any p o s i t i o n of the sticks the d i a g o n a l s b i s e c t each o t h e r . T h locus of the d i a g o n a l s i n t e r s e c t i o n , for a i fixed b a s e is easily seen from, th-- m o d e l . 4. The Kite: Join the unequal pairs of equal s t i c k s , s u c c e s s i v e l y , and f a s t e n elastic diagonals, The elasticskare always p e r p e n d i c u l a r for any p o s i t i o n of the s t i c k s • The l o c u s of the diagonals1 i n t e r s e c t i o n , w h e n the p o s i t i o n of one d i a g o n a l (b) is fixed i l l u s t r a t e s the p e r p e n d i c u l a r b i s e c t o r of a g i v e n line s e g m e n t . 5* Quadrilateral: Join the ends of four u n e a u a i sticks w i t h i n t e r l o c k e d eye h o o k s . Insert an eye h o o k a t e a c h m i d - p o i n t and t h r o u g h them ^ a s s , in o r d e r , an elastic l o o p * T h e loop forms a p a r a l l e l o g r a m no m a t t e r in w h a t p o s i t i o n , p l a n e or in s p a c e , the four st-cks are h o l d . 5f Triangle: On a d r a w i n g b o a r d , thumb tack the ends of two u n e q u a l elastic c o r d s , s e p a r a t e l y , ten u n i t ^ a p a r t * Connect the m i d - p o i n t s of the e l a s t i c s by a n o n - e l a s t i c cord or stick 5 u n i t s in l e n g t h . Joining the loose ends of the . elastics to a single p o i n t ancSpoving this p o i n t ts. to any p o s i t i o n in the p l a n e of the b o a ^ d so that a taut figure is f o r m e d , the 5 i n c h cord is always p a r a l l e l to the b a s e * What happens V in th.is same f i g u r e if the thumb tacks are -V 1 2 " apart? 7# Intuitive Geometry Board: D i v i d e a l a r g e board 50n x 20?r into u n i t s q u a r e s . On a lower h o r i z o n t a l line a t t a c h or p a s t e two p r o t r a c t o r s (celluloid or t r a n s p a r e n t if p o s s i b l e ) w i t h c e n t e r s 10 u n i t s a p a r t . To e a c h center a t t a c h m e t a l s t r i p s , d i v i d e d into u n i t s , and n u m b e r e d , 7«ero in e a c h case at the p r o t r a c t o r center, A s u r p r i s i n g l y l a r g e n u m b e r of t h e orems r e l a t i n g to t r i a n g l e s and p a r a l l e l l i n e s can be d i s c o v e r e d on this b o a r d . A sliding p r o t r a c t o r on one a^m can b e an added f e a t u r e . (See P l a t e I I , n o . 1 ) 8. Theorem Board: At the bottom center of a board 20n x 20I! p ^ i n t a b l a c k c i r c l e , r a d i u s 5?f. Around the b o a r d , around the c i r c l e , at the center,- and along a -vertical d i a m e t e r d r i l l small h o l e s , to fit golf t e e s . D r i l l as m a n y h o l e s a ^ p o s s i b l e ,

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