By Wygodski M.Ja.
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Mathematik ist eine vielseitige und lebendige Wissenschaft. Von den großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen zu den aktuellen mathematischen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten.
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In repainting a house, Mr. Linseed e n c o u n t e r e d the difficulty s h o w n in the illustration. On o n e s i d e , a p r o j e c t i n g b a y w i n d o w p r e v e n t e d h i s s e t t i n g h i s 20f o o t l a d d e r close t o the w a l l . H o w e v e r , he f o u n d t h a t h e could 56 GEOMETRICAL PUZZLES 58 r e a c h some p a r t of the wall a b o v e the w i n d o w b y p l a c i n g his l a d d e r snugly against the b a y a n d also against the wall. T h e o u t e r b a t t e n of t h e b a y w i n d o w a g a i n s t w h i c h t h e l a d d e r rests is 3 f e e t f r o m t h e w a l l a n d 12 f e e t a b o v e t h e g r o u n d .
So saying, Cutler drew a large block-letter capital A. "Let's see you divide this A into four parts which can be put together to make a Z. " Tyrus accepted the challenge and set to work. His first two DISSECTION OF PLANE FIGURES attempts of the A found a you find 43 were ruled out, because each time he had to turn a piece over to make it fit into the Z. But on the third try he solution which Cutler had to admit was correct. Can it? 88. THE MITRE FALLACY. Sam Loyd, who invented many ingenious puzzles, once propounded the following: A carpenter has a mitre, of the shape shown in the diagram — a square with one quarter cut out.
C L O C K SEMAPHORE, (a) At what time between two and three o'clock will the minute hand be as far from V I as the hour hand is from XII ? (b) What is the first time after noon that the minute hand has as far to go to reach XII as the hour hand has passed XII? V. Dissection of Plane Figures 82. C H A N G I N G A RECTANGLE TO A SQUARE. One of the basic dissection problems is to change a rectangle into a square. The general method is illustrated in the diagram. Given the rectangle ABCD, first find the length of side of the square of equal area.