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ElaKiri Talk!
Puzzle - Geometry
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<blockquote data-quote="imhotep" data-source="post: 29858313" data-attributes="member: 562115"><p>Nice... Very good effort. This is one of the solutions. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite22" alt="(y)" title="Thumbs up (y)" loading="lazy" data-shortname="(y)" /></p><hr /><p>Here are the solutions. If anyone finds others please post..</p><p></p><p>Geometrical Solutions. - The first is the one [USER=236390]@nlasasatha[/USER] posted.</p><p></p><p>1)</p><p></p><p><a href="https://imgbox.com/yxxvcqAV" target="_blank"><img src="https://thumbs2.imgbox.com/1b/27/yxxvcqAV_t.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p>2) Alternate Geometric</p><p></p><p><a href="https://imgbox.com/P8YWN30t" target="_blank"><img src="https://thumbs2.imgbox.com/c3/0c/P8YWN30t_t.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p></p><p>Non-Geometrical Solutions</p><p></p><p>3)</p><p></p><p><a href="https://imgbox.com/sximmUId" target="_blank"><img src="https://thumbs2.imgbox.com/e8/c9/sximmUId_t.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p>Imagine the squares are in the complex plane, Origin, the lower left hand vertex. Horizontal the real axis and Vertical<em> i </em>axis. Let Z1, Z2 and Z3 represent three complex numbers in an Argand diagram.</p><p>Z1 = 3+i, Z2 = 2+i and Z3 = 1 +i,</p><p></p><p>Our angles of interest are the "Arguments" of these three complex numbers. Now we know that if we multiply complex numbers then the Arguments gets added.</p><p>I leave it to you to multiply Z1, Z2 and Z3. You will get the answer 10i. So the argument of the multiplication of the three numbers is π/2.</p><p>Thus A + B + C = π/2</p><p></p><p>4) Trigonometry</p><p></p><p>The other solution is the one I already mentioned above using Trignometry and the property of the addition of two inverse tangents.</p><p>A + B = tan^-1(1/3)+tan^-1(1/2) = π/4 = C</p><p>------ <span style="font-size: 10px">Post added on [DATETIME="UT"]1717288036[/DATETIME]</span></p></blockquote><p></p>
[QUOTE="imhotep, post: 29858313, member: 562115"] Nice... Very good effort. This is one of the solutions. (y) [HR][/HR] Here are the solutions. If anyone finds others please post.. Geometrical Solutions. - The first is the one [USER=236390]@nlasasatha[/USER] posted. 1) [URL='https://imgbox.com/yxxvcqAV'][IMG]https://thumbs2.imgbox.com/1b/27/yxxvcqAV_t.jpg[/IMG][/URL] 2) Alternate Geometric [URL='https://imgbox.com/P8YWN30t'][IMG]https://thumbs2.imgbox.com/c3/0c/P8YWN30t_t.jpg[/IMG][/URL] Non-Geometrical Solutions 3) [URL='https://imgbox.com/sximmUId'][IMG]https://thumbs2.imgbox.com/e8/c9/sximmUId_t.jpg[/IMG][/URL] Imagine the squares are in the complex plane, Origin, the lower left hand vertex. Horizontal the real axis and Vertical[I] i [/I]axis. Let Z1, Z2 and Z3 represent three complex numbers in an Argand diagram. Z1 = 3+i, Z2 = 2+i and Z3 = 1 +i, Our angles of interest are the "Arguments" of these three complex numbers. Now we know that if we multiply complex numbers then the Arguments gets added. I leave it to you to multiply Z1, Z2 and Z3. You will get the answer 10i. So the argument of the multiplication of the three numbers is π/2. Thus A + B + C = π/2 4) Trigonometry The other solution is the one I already mentioned above using Trignometry and the property of the addition of two inverse tangents. A + B = tan^-1(1/3)+tan^-1(1/2) = π/4 = C ------ [SIZE=2]Post added on [DATETIME="UT"]1717288036[/DATETIME][/SIZE] [/QUOTE]
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