( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39
Call Stack
#	Time	Memory	Function	Location
1	0.0001	366088	{main}( )	...\index.php:0
2	0.0113	668248	SpotPage_editspot->render( )	...\index.php:327
3	0.0167	766832	str_replace( $search = '[br]', $replace = '\n', $subject = ['category' => '0', 'website' => '', 'image' => ['height' => '164', 'width' => '475', 'segment' => [...]], 'sabnzbdurl' => '', 'messageid' => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 'searchurl' => '', 'description' => 'Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was'..., 'sub' => '', 'filesize' => '54109128', 'poster' => 'TarkusTWS', 'tag' => 'NFL', 'nzb' => [0 => 'MEbyJDt3uAkCxMWYgO2fq@spot.net'], 'title' => 'Mathematics - An Illustrated History of Numbers', 'filename' => '', 'newsgroup' => '', 'subcata' => 'a11\|', 'subcatb' => 'b3\|', 'subcatc' => 'c10\|', 'subcatd' => '', 'subcatz' => 'z2\|', 'created' => '1645613841', 'key' => '7', 'prevMsgids' => [], 'newsreader' => 'Spotnet 1.9.0.7', 'id' => '2078495', 0 => '2078495', 1 => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 2 => '0', 3 => 'TarkusTWS', 4 => 'a11\|', 5 => 'b3\|', 6 => 'c10\|', 7 => '', 8 => 'z2\|', 9 => 'Mathematics - An Illustrated History of Numbers', 10 => 'NFL', 'stamp' => '1645613840', 11 => '1645613840', 'moderated' => NULL, 12 => NULL, 'rating' => '0', 13 => '0', 'commentcount' => '0', 14 => '0', 'reportcount' => '0', 15 => '0', 16 => '54109128', 'spotterid' => 'zBjc6A', 17 => 'zBjc6A', 'editstamp' => NULL, 18 => NULL, 'editor' => NULL, 19 => NULL, 'downloadstamp' => NULL, 20 => NULL, 'watchstamp' => NULL, 21 => NULL, 'seenstamp' => '1793057455', 22 => '1793057455', 'verified' => '1', 23 => '1', 'user-signature' => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 24 => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 'user-key' => ['exponent' => 'AQAB', 'modulo' => '3yEDLsqXWt2JFhrDa2rk7mk23g752GYsql1jAFWRVyDNydQk25WxhE1VsImKG6iv'], 25 => 'YToyOntzOjg6ImV4cG9uZW50IjtzOjQ6IkFRQUIiO3M6NjoibW9kdWxvIjtzOjY0OiIzeUVETHNxWFd0MkpGaHJEYTJyazdtazIzZzc1MkdZc3FsMWpBRldSVnlETnlkUWsyNVd4aEUxVnNJbUtHNml2Ijt9', 'xml-signature' => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 26 => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 'fullxml' => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 27 => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 'listidtype' => NULL, 28 => NULL] )	...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39

Call Stack

Time

Memory

Function

Location

0.0001

366088

{main}( )

...\index.php:0

0.0113

668248

SpotPage_editspot->render( )

...\index.php:327

0.0167

766832

str_replace( $search = '[br]', $replace = '\n', $subject = ['category' => '0', 'website' => '', 'image' => ['height' => '164', 'width' => '475', 'segment' => [...]], 'sabnzbdurl' => '', 'messageid' => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 'searchurl' => '', 'description' => 'Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was'..., 'sub' => '', 'filesize' => '54109128', 'poster' => 'TarkusTWS', 'tag' => 'NFL', 'nzb' => [0 => 'MEbyJDt3uAkCxMWYgO2fq@spot.net'], 'title' => 'Mathematics - An Illustrated History of Numbers', 'filename' => '', 'newsgroup' => '', 'subcata' => 'a11|', 'subcatb' => 'b3|', 'subcatc' => 'c10|', 'subcatd' => '', 'subcatz' => 'z2|', 'created' => '1645613841', 'key' => '7', 'prevMsgids' => [], 'newsreader' => 'Spotnet 1.9.0.7', 'id' => '2078495', 0 => '2078495', 1 => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 2 => '0', 3 => 'TarkusTWS', 4 => 'a11|', 5 => 'b3|', 6 => 'c10|', 7 => '', 8 => 'z2|', 9 => 'Mathematics - An Illustrated History of Numbers', 10 => 'NFL', 'stamp' => '1645613840', 11 => '1645613840', 'moderated' => NULL, 12 => NULL, 'rating' => '0', 13 => '0', 'commentcount' => '0', 14 => '0', 'reportcount' => '0', 15 => '0', 16 => '54109128', 'spotterid' => 'zBjc6A', 17 => 'zBjc6A', 'editstamp' => NULL, 18 => NULL, 'editor' => NULL, 19 => NULL, 'downloadstamp' => NULL, 20 => NULL, 'watchstamp' => NULL, 21 => NULL, 'seenstamp' => '1793057455', 22 => '1793057455', 'verified' => '1', 23 => '1', 'user-signature' => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 24 => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 'user-key' => ['exponent' => 'AQAB', 'modulo' => '3yEDLsqXWt2JFhrDa2rk7mk23g752GYsql1jAFWRVyDNydQk25WxhE1VsImKG6iv'], 25 => 'YToyOntzOjg6ImV4cG9uZW50IjtzOjQ6IkFRQUIiO3M6NjoibW9kdWxvIjtzOjY0OiIzeUVETHNxWFd0MkpGaHJEYTJyazdtazIzZzc1MkdZc3FsMWpBRldSVnlETnlkUWsyNVd4aEUxVnNJbUtHNml2Ijt9', 'xml-signature' => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 26 => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 'fullxml' => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 27 => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 'listidtype' => NULL, 28 => NULL] )

...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39
Call Stack
#	Time	Memory	Function	Location
1	0.0001	366088	{main}( )	...\index.php:0
2	0.0113	668248	SpotPage_editspot->render( )	...\index.php:327
3	0.0167	766832	str_replace( $search = '[br]', $replace = '\n', $subject = ['category' => '0', 'website' => '', 'image' => ['height' => '164', 'width' => '475', 'segment' => [...]], 'sabnzbdurl' => '', 'messageid' => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 'searchurl' => '', 'description' => 'Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was'..., 'sub' => '', 'filesize' => '54109128', 'poster' => 'TarkusTWS', 'tag' => 'NFL', 'nzb' => [0 => 'MEbyJDt3uAkCxMWYgO2fq@spot.net'], 'title' => 'Mathematics - An Illustrated History of Numbers', 'filename' => '', 'newsgroup' => '', 'subcata' => 'a11\|', 'subcatb' => 'b3\|', 'subcatc' => 'c10\|', 'subcatd' => '', 'subcatz' => 'z2\|', 'created' => '1645613841', 'key' => '7', 'prevMsgids' => [], 'newsreader' => 'Spotnet 1.9.0.7', 'id' => '2078495', 0 => '2078495', 1 => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 2 => '0', 3 => 'TarkusTWS', 4 => 'a11\|', 5 => 'b3\|', 6 => 'c10\|', 7 => '', 8 => 'z2\|', 9 => 'Mathematics - An Illustrated History of Numbers', 10 => 'NFL', 'stamp' => '1645613840', 11 => '1645613840', 'moderated' => NULL, 12 => NULL, 'rating' => '0', 13 => '0', 'commentcount' => '0', 14 => '0', 'reportcount' => '0', 15 => '0', 16 => '54109128', 'spotterid' => 'zBjc6A', 17 => 'zBjc6A', 'editstamp' => NULL, 18 => NULL, 'editor' => NULL, 19 => NULL, 'downloadstamp' => NULL, 20 => NULL, 'watchstamp' => NULL, 21 => NULL, 'seenstamp' => '1793057455', 22 => '1793057455', 'verified' => '1', 23 => '1', 'user-signature' => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 24 => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 'user-key' => ['exponent' => 'AQAB', 'modulo' => '3yEDLsqXWt2JFhrDa2rk7mk23g752GYsql1jAFWRVyDNydQk25WxhE1VsImKG6iv'], 25 => 'YToyOntzOjg6ImV4cG9uZW50IjtzOjQ6IkFRQUIiO3M6NjoibW9kdWxvIjtzOjY0OiIzeUVETHNxWFd0MkpGaHJEYTJyazdtazIzZzc1MkdZc3FsMWpBRldSVnlETnlkUWsyNVd4aEUxVnNJbUtHNml2Ijt9', 'xml-signature' => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 26 => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 'fullxml' => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 27 => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 'listidtype' => NULL, 28 => NULL] )	...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39

Call Stack

Time

Memory

Function

Location

0.0001

366088

{main}( )

...\index.php:0

0.0113

668248

SpotPage_editspot->render( )

...\index.php:327

0.0167

766832

...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39
Call Stack
#	Time	Memory	Function	Location
1	0.0001	366088	{main}( )	...\index.php:0
2	0.0113	668248	SpotPage_editspot->render( )	...\index.php:327
3	0.0167	766832	str_replace( $search = '[br]', $replace = '\n', $subject = ['category' => '0', 'website' => '', 'image' => ['height' => '164', 'width' => '475', 'segment' => [...]], 'sabnzbdurl' => '', 'messageid' => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 'searchurl' => '', 'description' => 'Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was'..., 'sub' => '', 'filesize' => '54109128', 'poster' => 'TarkusTWS', 'tag' => 'NFL', 'nzb' => [0 => 'MEbyJDt3uAkCxMWYgO2fq@spot.net'], 'title' => 'Mathematics - An Illustrated History of Numbers', 'filename' => '', 'newsgroup' => '', 'subcata' => 'a11\|', 'subcatb' => 'b3\|', 'subcatc' => 'c10\|', 'subcatd' => '', 'subcatz' => 'z2\|', 'created' => '1645613841', 'key' => '7', 'prevMsgids' => [], 'newsreader' => 'Spotnet 1.9.0.7', 'id' => '2078495', 0 => '2078495', 1 => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 2 => '0', 3 => 'TarkusTWS', 4 => 'a11\|', 5 => 'b3\|', 6 => 'c10\|', 7 => '', 8 => 'z2\|', 9 => 'Mathematics - An Illustrated History of Numbers', 10 => 'NFL', 'stamp' => '1645613840', 11 => '1645613840', 'moderated' => NULL, 12 => NULL, 'rating' => '0', 13 => '0', 'commentcount' => '0', 14 => '0', 'reportcount' => '0', 15 => '0', 16 => '54109128', 'spotterid' => 'zBjc6A', 17 => 'zBjc6A', 'editstamp' => NULL, 18 => NULL, 'editor' => NULL, 19 => NULL, 'downloadstamp' => NULL, 20 => NULL, 'watchstamp' => NULL, 21 => NULL, 'seenstamp' => '1793057455', 22 => '1793057455', 'verified' => '1', 23 => '1', 'user-signature' => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 24 => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 'user-key' => ['exponent' => 'AQAB', 'modulo' => '3yEDLsqXWt2JFhrDa2rk7mk23g752GYsql1jAFWRVyDNydQk25WxhE1VsImKG6iv'], 25 => 'YToyOntzOjg6ImV4cG9uZW50IjtzOjQ6IkFRQUIiO3M6NjoibW9kdWxvIjtzOjY0OiIzeUVETHNxWFd0MkpGaHJEYTJyazdtazIzZzc1MkdZc3FsMWpBRldSVnlETnlkUWsyNVd4aEUxVnNJbUtHNml2Ijt9', 'xml-signature' => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 26 => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 'fullxml' => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 27 => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 'listidtype' => NULL, 28 => NULL] )	...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39

Call Stack

Time

Memory

Function

Location

0.0001

366088

{main}( )

...\index.php:0

0.0113

668248

SpotPage_editspot->render( )

...\index.php:327

0.0167

766832

...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39
Call Stack
#	Time	Memory	Function	Location
1	0.0001	366088	{main}( )	...\index.php:0
2	0.0113	668248	SpotPage_editspot->render( )	...\index.php:327
3	0.0167	766832	str_replace( $search = '[br]', $replace = '\n', $subject = ['category' => '0', 'website' => '', 'image' => ['height' => '164', 'width' => '475', 'segment' => [...]], 'sabnzbdurl' => '', 'messageid' => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 'searchurl' => '', 'description' => 'Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was'..., 'sub' => '', 'filesize' => '54109128', 'poster' => 'TarkusTWS', 'tag' => 'NFL', 'nzb' => [0 => 'MEbyJDt3uAkCxMWYgO2fq@spot.net'], 'title' => 'Mathematics - An Illustrated History of Numbers', 'filename' => '', 'newsgroup' => '', 'subcata' => 'a11\|', 'subcatb' => 'b3\|', 'subcatc' => 'c10\|', 'subcatd' => '', 'subcatz' => 'z2\|', 'created' => '1645613841', 'key' => '7', 'prevMsgids' => [], 'newsreader' => 'Spotnet 1.9.0.7', 'id' => '2078495', 0 => '2078495', 1 => 'T5cmRqsnd1oCxMWYgrRK3@spot.net', 2 => '0', 3 => 'TarkusTWS', 4 => 'a11\|', 5 => 'b3\|', 6 => 'c10\|', 7 => '', 8 => 'z2\|', 9 => 'Mathematics - An Illustrated History of Numbers', 10 => 'NFL', 'stamp' => '1645613840', 11 => '1645613840', 'moderated' => NULL, 12 => NULL, 'rating' => '0', 13 => '0', 'commentcount' => '0', 14 => '0', 'reportcount' => '0', 15 => '0', 16 => '54109128', 'spotterid' => 'zBjc6A', 17 => 'zBjc6A', 'editstamp' => NULL, 18 => NULL, 'editor' => NULL, 19 => NULL, 'downloadstamp' => NULL, 20 => NULL, 'watchstamp' => NULL, 21 => NULL, 'seenstamp' => '1793057455', 22 => '1793057455', 'verified' => '1', 23 => '1', 'user-signature' => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 24 => 'mnBcXX4eezIeWLmtXGaOp9gBTaT6APVIwN+Mvi0mGXR4dbULo22TDd0XOqA44E54===', 'user-key' => ['exponent' => 'AQAB', 'modulo' => '3yEDLsqXWt2JFhrDa2rk7mk23g752GYsql1jAFWRVyDNydQk25WxhE1VsImKG6iv'], 25 => 'YToyOntzOjg6ImV4cG9uZW50IjtzOjQ6IkFRQUIiO3M6NjoibW9kdWxvIjtzOjY0OiIzeUVETHNxWFd0MkpGaHJEYTJyazdtazIzZzc1MkdZc3FsMWpBRldSVnlETnlkUWsyNVd4aEUxVnNJbUtHNml2Ijt9', 'xml-signature' => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 26 => 'VWSO3mKXj/GEaDZKItu8pKngvDNIeBh1Jk3fcomEPEUQBFKMVhM35cXzWKQ3aVmS===', 'fullxml' => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 27 => '<?xml version="1.0"?>\n<Spotnet><Posting><Key>7</Key><Created>1645613841</Created><Poster>TarkusTWS</Poster><Tag>NFL</Tag><Title>Mathematics - An Illustrated History of Numbers</Title><Description>Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating cha'..., 'listidtype' => NULL, 28 => NULL] )	...\SpotPage_editspot.php:39

( ! ) Warning: Array to string conversion in C:\wamp64\www\lib\page\SpotPage_editspot.php on line 39

Call Stack

Time

Memory

Function

Location

0.0001

366088

{main}( )

...\index.php:0

0.0113

668248

SpotPage_editspot->render( )

...\index.php:327

0.0167

766832

...\SpotPage_editspot.php:39

( ! ) Warning: Cannot modify header information - headers already sent by (output started at C:\wamp64\www\lib\page\SpotPage_editspot.php:39) in C:\wamp64\www\lib\page\SpotPage_Abs.php on line 63
Call Stack
#	Time	Memory	Function	Location
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{main}( )

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Category

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Titel

Description

Legend has it that the first magic square, where all lines and diagonals add up to the same figure, was revealed more than 2,000 years ago when a river turtle appeared to have ancient Chinese numerals inscribed on sections of its shell. Patterns are everywhere in nature, and counting, measuring, and calculating changes are as old as civilization itself, as are many of the theorems and laws of math. The Pythagorean Theorem was used to plot out fields for planting crops before the ancient Greek Pythagoras was even born, but the story begins long before that, with tally marks on rock and bone surviving from the Stone Age. Here is the essential guide to mathematics, an authoritative reference book and timeline that explores the work of history s greatest mathematicians. From the teasing genius of Pierre de Fermat, who said he knew the answers but rarely gave them up, to the fractal pattern discovered by Waclaw Sierpinski now used to plan the route a mailman takes, here are 100 landmark moments in this intensely rigorous discipline, seen through the eyes of the people who lived them. Glimpse the abstract landscape of infinite numbers and multi-dimensional shapes as you learn about the most famous math men of all. Pythagoras had a love of numbers so strong it led to a violent death. Then there is Fibonacci, whose guide for bookkeepers changed the way we add and Descartes, who took inspiration from a fly to convert numbers into shapes and back again, changing math forever. Over many centuries, great minds puzzled over the evidence and, step-by-step, edged ever closer to the truth. Behind every one of these breakthrough moments there s a story about a confounding puzzle that became a discovery and changed the way we see the world. Here are one hundred of the most significant and we call these Ponderables. In Mathematics: An Illustrated History of Numbers, you ll get a peak into the Imponderables, too, the mysteries yet to be solved that will one day lead great thinkers forward to an even greater understanding of the universe. Includes a removable fold-out concertina neatly housed in the back of the book. This fold-out provides a 12-page Timeline History of Mathematics that embeds the story in historical context and shows Who Did What When at a glance. The reverse side features some of the greatest mathematical enigmas and interesting facts about the world of numbers.

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