Repository: UIHistories Project: Mathematical Models Construction and Use of Mathematical Models (Fehr & Hildebrandt) [PAGE 10]

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symmetrieally placed. W i t h r e d and b l a c k c o l ored e l a s t i c , and g o l f tees w i t h l e t t e r e d h e a d s , any p l a n e g e o m e t r y t h e o r e m r e l a t i n g to a single figure can be r e p r e s e n t e d . (See P l a t e I I , n o , 6 ) Many other models on angle measurement, s i m i l a r i t y , c i r c l e s , the P y t h a g o r e a n t h e o r e m , e t c . , are d e s c r i b e d in v a r i o u s texts and f o r m e x c e l l e n t teaching d e v i c e s . 9, Solid Geometry Theorem Mod I s : In the b e g i n n i n g of the study ojjfeolid g e o m e t r y , m o d e l s o f the t h e o r e m s are e s p e c i a l l y I m p o r t a n t , 'They serve the same purp ose as a b l a c k b o a r d d r a w i n g of a f i g u r e ip p l a n e g e o m e t r y , w h i c h is e s s e n t i a l l y a m o d e l for the t h e o r e m , T e m p e r a ^ v m o d e l s can e asily be m a d e f r o m such m a t erlals as c a r d b o a r d , pencils^ k n l t t i n g needles,, thin s t i c k s , c o r k , s t r i n g , and p a s t e . W i t h these m a t e r ials every student can m a k e h i s own m o d e l of the t h e o r e m u n d e r . d i s c u s s i o n . Permanent models can be m a d e f r o m w o o d , g l a s s , h e a v y c e l l u l o i d or w i r e me^tu (See Plate I I , n o , 3 ) 10* G e o m e t r i c Solids*. M o d e l s of p r i s m s , p y r a m i d s , c o n e s , c y l i n d e r s and s p h e r e s can. b e turned out of m e t a 1 or w o o d on a lathe In the school s h o p , S e c t i o n s of these so lids ( r i g h t , obl i q u e , c i r c u l a r , e l l i p t i c a l , e t c . ) can b e sa:-ed t h r o u g h , the cut filled w i t h shellac and the p a r t s c o n n e c t e d b y c o u n t e r - s u n k pins• In Junior H i g h S c h o o l these m o d e l s can b e m e a s u r e d , to d e t e r m i n e ar ea and v o l u m e r e ~ l a t l o n s as w e l l as to establ ish the c o n c e p t of a p p r o x i m a t e c o m p u t a t i o n and. d e g r e e of a c c u r a c y . (See Plate I, n o . 8 ) T h e m o d e l s can b o m a d e out of slender rods w o o d e n or w i r e , w i t h the ends sealed w i t h w a x , glue or s o l d e r . S u c h m o d e l s aid in d i s c o v e r i n g aid v i s u a l i z i n g d i a g o n a l and Interior r e l a t i o n ships, (See P l a t e I I , n o , 4 ) The solids can b m a d e out of sheeted tin or '"'olluloid, w i t h one p a r t o p e n , and in this m a n n e r w i t h the u s e of sand or l i q u i d , b e used/co e s t a b l i s h v o l u m e r e l a t i o n s , as w e l l as\bo afford an interior v i e w of the solids. C e l l u l o i d m o d e l s of i n t e r s e c t i n g solid s, such as two c y l i n d e r s , are valuable, as\such i n t e r s e c t i o n s ar e e x c e e d i n g l y diff i c u l t to v i s u a l i z e • (See P l a t e I, n o , 5 ) 11* Soap b u b b l e f i g u r e s : The sphere and I n t e r s e c t i n g spheres are easy to m a k e f r o m a h o l l o w tube and soap w a t e r . A regular t e t r a h e d r o n , c o n s t r u c t e d w i t h six t h i n m e t a l r o d s as edges aid a t t a c h e d to a slender rod at one v e r t e x , w h e n d i p p e d in a soap solution, w i l l p r o d u c e a b u b b l e In the f o r m of^an I n t r a v e r t e d t e t r a h e d r o n , (See P l a t e I, n o . 2 ) A cube s i m i l a r l y constructed^ w i l l p r o d u c e an e v e n m o r e s t r i k i n g g e o m e t r i c space 'n/ j * surfacef *<L I