Task: Sentiment Analysis
Input (English): Engaging exercises to train your intuition . Famous mathematicians have often emphasized the role of visual intuition;  e.g., Hilbert: &quot;Who does not always use along with the double  inequality a &gt; b &gt; c the picture of three points following one  another on a straight line as the geometrical picture of the idea  &quot;between&quot;? Who does not make use of drawings of segments and  rectangles enclosed in one another, when it is required to prove with  perfect rigor a difficult theorem on the continuity of functions or the  existence of points of condensation?&quot; (from his famous address at the  1900 International Congress). This book is a collection of well over 100  one-page proofs, collected from various sources. The topics range from  number theory to calculus, and most of them require no advanced  mathematics. Typically there is a statement of a result, with a labelled  diagram showing how it is &quot;proved&quot;; in some cases there are a few  auxiliary equations along with the picture. These are not simple, often  requiring quite a bit of thought before the &quot;Aha!&quot; moment.  Working through them is a valuable exercise for the student of  mathematics--having seen, e.g., six different visual proofs of the  Pythagorean theorem, one comes to really *understand* the result, not just  &quot;follow the logic&quot;. I have not encountered any better way than  this book to &quot;see&quot; how mathematical truth is discovered and  proved. It can be valuable as a supplement to courses through precalculus  and elementary calculus. Perhaps one of its best uses is to inspire  teachers to present results in a more lively way then  &quot;definition-theorem-proof&quot; or &quot;just memorize it&quot;
Output (English): POS