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used cross-sections and transparent layers to show body intricacies","Leonardo's studies of the heart prefigured modern cardiology",1,{"id":37,"data":38,"type":39,"maxContentLevel":19,"version":35},"89b6c1ce-a5f7-408c-a354-b3578ceb41c9",{"type":39,"intro":40},10,[41,42],"What drove Leonardo to study anatomy despite religious controversies?","How did Leonardo's anatomical studies influence his artistry?",[44,58,63,68,81],{"id":45,"data":46,"type":35,"maxContentLevel":19,"version":25,"reviews":49},"467dc977-64a0-4ea9-85a1-ec2016dd7118",{"type":35,"markdownContent":47,"audioMediaId":48},"The study of anatomy during the Renaissance was fraught with religious controversy. The Church generally frowned upon the dissection of human bodies, viewing it as a desecration of the sacred human form.\n\n![Graph](image://6edd5fd8-fafe-441f-a79b-0a6c5c5386a1 \"Leonardo's sketch of the major vessels of a human body, showing his interest in anatomy. Image: Public Domain via Wikimedia\")\n\nThis prohibition greatly hampered knowledge of anatomy during this time, and acquiring cadavers for research was a taboo often navigated by robbing graves illegally.\n\nSo why did da Vinci persevere?\n\nLeonardo’s insatiable curiosity in this area was rooted in his belief in the interconnectedness of art and nature. He saw the human body as a masterpiece of nature's design, a perfect blend of form and function, and sought to understand it in its entirety.\n\nThis fascination is visible in the intricate sketches of the human skull that he began drawing in 1489. The skull was one of his very first dissections.\n\n![Graph](image://5bb520cf-fb14-47b5-87c9-61cddc205f0d \"Da Vinci's sketch of the skull. Image: Leonardo da Vinci via Wikimedia\")\n\nIn these early anatomical manuscripts, he depicted the cranium divided into two sections: one showing the exterior with teeth and jaw and the other showing the cavities within them.","8f69b52b-02ac-4885-b2d2-68b35811689c",[50],{"id":51,"data":52,"type":53,"version":35,"maxContentLevel":19},"8a7236ee-7907-4d4a-9339-f31f107325b4",{"type":53,"reviewType":20,"spacingBehaviour":35,"clozeQuestion":54,"clozeWords":56},11,[55],"Leonardo's curiosity in anatomy was rooted in his belief in the interconnectedness of art and nature.",[57],"nature",{"id":59,"data":60,"type":35,"maxContentLevel":19,"version":25},"c1407598-b162-4017-a488-3a572aee3468",{"type":35,"markdownContent":61,"audioMediaId":62},"Leonardo's anatomical sketches are celebrated for their precision and attention to detail. They also often went beyond static depictions of the human body and often constituted studies of the body in motion.\n\nThis reflected da Vinci’s fascination with the unity of form and function.\n\n![Graph](image://3c4590f6-de0a-406d-a79b-a8503fa09441 \"The superficial anatomy of the shoulder and neck. Image: Public Domain via Wikimedia commons\")\n\nIn his sketches, Leonardo meticulously displayed the interplay of veins, arteries, muscles, internal organs, and bones. He typically portrayed the body’s intricacies through transparent layers, which afforded an “insight” into the organ through the use of sections in perspective.\n\nEven though his medical investigations remained private and went unpublished during his lifetime, the wealth of Leonardo’s drawings that have survived forged are still considered exemplars of scientific illustration.","1d72837d-1bb6-4e67-9dce-fdd35463a072",{"id":64,"data":65,"type":35,"maxContentLevel":19,"version":25},"484955a6-8495-49a8-a18c-c276705f28c6",{"type":35,"markdownContent":66,"audioMediaId":67},"Leonardo's detailed studies of the human skeleton, muscles, and internal organs garnered a great deal of valuable insights into the human body. His clever scientific illustration techniques - such as his use of cross-sections, transparent overlays, and perspective - have also stood the test of time.\n\nIn terms of medical progress, Leonardo was one of the first people to accurately represent the human spine in all its complexity.\n\n![Graph](image://2bde3ab6-fb48-4f15-bc48-1079981c38bb \"Leonardo's sketches of joints and skeletal muscle. Image: Tangopaso, Public domain, via Wikimedia Commons\")\n\nAdditionally, Leonardo's studies of the heart were so advanced that they prefigured modern cardiology.\n\nHis understanding of the heart's structure and function, as depicted in his sketches, was far ahead of his time. For example, he was aware of the four chambers of the heart, the existence of heart valves, and the important idea of coronary circulation.","e2b4b84f-eff0-4071-abff-6535b5129f00",{"id":69,"data":70,"type":35,"maxContentLevel":19,"version":20,"reviews":73},"0b8bcd9d-2e63-48af-9475-c8e374f0ec4c",{"type":35,"markdownContent":71,"audioMediaId":72},"One of Leonardo's most famous anatomical works is titled 'Studies of the Fetus in the Womb'. These two colored and annotated sketches were made around 1511 and provide a staggeringly detailed depiction of a fetus in utero.\n\n![Graph](image://57768032-fbd2-43fb-86c9-4a8fa98f3f6e \"Leonardo da Vinci's Studies of the Foetus in the Womb. Image: Leonardo da Vinci, Public domain, via Wikimedia Commons.\")\n\nThese sketches showcase Leonardo's innovative use of cross-sections and multiple perspectives - techniques he used to represent the complex structure of the dissected womb and the correctly positioned fetus within it.\n\nLeonardo accurately depicted the uterus as having a single chamber. This was in contrast to the prevailing belief that it had multiple chambers that divided fetuses into separate compartments in the case of twins!","e2620909-91c8-439f-aeaa-c8b886614203",[74],{"id":75,"data":76,"type":53,"version":35,"maxContentLevel":19},"474977b3-c9f2-4d44-9898-97b8d5f6935d",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":77,"activeRecallAnswers":79},[78],"What did Leonardo understand about a human uterus that went against prevailing beliefs at the time?",[80],"The uterus as having a single chamber, as opposed to had multiple chambers that were used in the case of twins",{"id":82,"data":83,"type":35,"maxContentLevel":19,"version":25,"reviews":86},"f9af56c5-6887-4fbe-99dc-578eb0fed413",{"type":35,"markdownContent":84,"audioMediaId":85},"Leonardo's anatomical studies enabled him to depict the human form with unparalleled realism and accuracy. His enriched understanding of both the structure and function of the human body, allowed him to confidently portray human figures in an array of expressive poses and actions, capturing the subtleties of movement and posture.\n\nHis understanding of facial muscles and their connections also made da Vinci skilled in conveying emotions, making ready use of the play of light and shadow over muscles, and bones.\n\n![Graph](image://6a91cc70-4252-4ee7-a103-f5c6d8ed92cc \"Head and shoulders of a man, seen from the left, showing the muscles of the neck, chest and shoulder. Etching by Wenceslaus Hollar after Leonardo da Vinci, 1651. Image: Wellcome Collection, CC BY 4.0 \u003Chttps://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons. \")\n\nCombined with his skilled representation of the texture and surface of the skin, this anatomical realism adds beautiful depth to the faces in da Vinci’s paintings.","c0e19f90-d177-4577-bac7-5ece5116c24b",[87],{"id":88,"data":89,"type":53,"version":35,"maxContentLevel":19},"71b14776-6163-426a-889d-00febd186338",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":90,"activeRecallAnswers":92},[91],"What did Leonardo's understanding of facial muscles and their connections allow him to do?",[93],"Convey emotions, making use of the play of light and shadow over muscles, and bones",{"id":95,"data":96,"type":25,"version":19,"maxContentLevel":19,"summaryPage":98,"introPage":106,"pages":112},"59fd3ba0-3020-4a56-8012-bc866ce7c649",{"type":25,"title":97},"The Vitruvian Man",{"id":99,"data":100,"type":19,"maxContentLevel":19,"version":35},"4018b769-e0da-4671-bf1c-68285c635381",{"type":19,"summary":101},[102,103,104,105],"Renaissance artists believed the human form reflected divine perfection","Leonardo's Vitruvian Man is a famous drawing of ideal human proportions","The golden ratio is about 1618 and appears in the Vitruvian Man","The Fibonacci sequence is linked to the golden ratio and found in nature",{"id":107,"data":108,"type":39,"maxContentLevel":19,"version":35},"6aa29637-72d3-4e71-ba9c-5a5cbca6c513",{"type":39,"intro":109},[110,111],"What inspired Leonardo's Vitruvian Man sketch?","How does the Fibonacci sequence relate to the golden ratio?",[113,133,166,183],{"id":114,"data":115,"type":35,"maxContentLevel":19,"version":19,"reviews":118},"7fd1b967-62e9-48d8-b29b-25f68d9e4b97",{"type":35,"markdownContent":116,"audioMediaId":117},"The study of human proportion wasn’t a new concept. The ancient Greeks and Romans also studied the human form in great detail, producing some of the most accurate sculptures that remain to this day.\n\nHowever, during the Renaissance, these studies took on a new lease of life, as the human form was believed to reflect the divine perfection of the universe, as created by God.\n\nProminent artists such as Albrecht Dürer conducted extensive studies on human proportions, aiming to discover a mathematical and aesthetic ideal.\n\n![Graph](image://a028e2fe-0633-42cd-a87d-ac1e1084dac5 \"A portrait of Albrecht Dürer. Image: Public Domain via Wikimedia\")\n\n![Graph](image://a48a278a-7d09-4ac9-91da-e9c921797e8b \"A page from Four Books on Human Proportion. Image: Metropolitan Museum of Art, CC0 \t\nhttps://creativecommons.org/publicdomain/zero/1.0/ via Wikimedia commons.\")\n\nBy far the most famous product of the study of human proportion during the Renaissance is the 'Vitruvian Man', a drawing by Leonardo.\n\nIt’s a work that is widely considered to be among the all-time most iconic images in Western civilization.\n\n![Graph](image://a9274ed9-ca4f-4613-89bf-12812baa71b5 \"The Vitruvian Man by Leonardo da Vinci. Image: Public Domain via Wikimedia\")\n\nIt’s dated to around 1490 and depicts a nude man in two superimposed positions with his arms and legs apart, inscribed in a circle and square. It is an attempt to represent the mathematical principles that govern the proportions of the human body.","90146a9f-4d91-4375-90b2-8f3a6256891d",[119,126],{"id":120,"data":121,"type":53,"version":35,"maxContentLevel":19},"68efe77f-aed8-4136-88c7-62bd2b57ed2f",{"type":53,"reviewType":20,"spacingBehaviour":35,"clozeQuestion":122,"clozeWords":124},[123],"The \"Vitruvian Man\" is a famous drawing by Leonardo, depicting a mathematical representation of human proportions.",[125],"Vitruvian Man",{"id":127,"data":128,"type":53,"version":35,"maxContentLevel":19},"3f91699b-5f30-4bb6-9f02-9cf411c52a48",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":129,"activeRecallAnswers":131},[130],"What does the “Vitruvian Man” depict?",[132],"A nude man in two superimposed positions with his arms and legs apart, inscribed in a circle and square",{"id":134,"data":135,"type":35,"maxContentLevel":19,"version":25,"reviews":138},"0adaea56-8dcf-4cf5-87e1-d210fc39e1ee",{"type":35,"markdownContent":136,"audioMediaId":137},"The drawing of the 'Vitruvian Man' was named after the ancient Roman architect Vitruvius, who lived during the 1st century BC. Vitruvius is best known for his multi-volume treatise titled *De Architectura*.\n\nThis treatise, which is the only treatise on architecture to have survived from antiquity, outlined his principles governing Greek and Roman buildings, as well as the ideal proportions of the human body.\n\n![Graph](image://91e742c3-36c8-4800-9cfb-0db05ba5fa88 \"Italian translation of De Architectura. Image: Metropolitan Museum of Art, CC0 \t\nhttps://creativecommons.org/publicdomain/zero/1.0/ via Wikimedia commons.\")\n\nLittle is known with certainty about Vitruvius’ life, but his discussion of perfect proportion in architecture and the human body directly inspired Leonardo’s sketch.\n\nLeonardo was a great admirer of Vitruvius, and he sought to visually represent the architect's concept of the proportionally ideal human body in his drawing.","a76562ab-3804-4fe7-ba70-3cff494ac57b",[139,159],{"id":140,"data":141,"type":53,"version":35,"maxContentLevel":19},"976d5e1a-4dda-426a-a8b4-381040fe048e",{"type":53,"reviewType":19,"spacingBehaviour":35,"collapsingSiblings":142,"multiChoiceQuestion":146,"multiChoiceCorrect":148,"multiChoiceIncorrect":150,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6,"matchPairsQuestion":154,"matchPairsPairs":156},[143,144,145],"edcdfc9f-2fc5-4643-8ada-f4e4a641160d","8fe193d7-cb9a-4030-818e-42056144c047","7d44e5e4-d8eb-4e66-b116-9cd79a1f80f9",[147],"Who was the Ancient Roman architect who lived during the 1st century BC?",[149],"Vitruvius",[151,152,153],"Pompeo Leoni","Francesco del Giocondo","Verrocchio",[155],"Match the pairs below:",[157],{"left":149,"right":158,"direction":19},"Ancient Roman architect, lived during the 1st century BC",{"id":160,"data":161,"type":53,"version":35,"maxContentLevel":19},"e2b66277-dd21-484a-ae2d-c05b03155798",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":162,"activeRecallAnswers":164},[163],"What is the name of the multi-volume treatise by Vitruvius that outlined his principles governing Greek and Roman buildings, as well as the ideal proportions of the human body?",[165],"De Architectura",{"id":167,"data":168,"type":35,"maxContentLevel":19,"version":19,"reviews":171},"eb9fe30d-4aae-474e-8a28-91e0c286c71a",{"type":35,"markdownContent":169,"audioMediaId":170},"The Vitruvian Man is known for exhibiting what’s known as the '**golden ratio**' in the man's height relative to the distance between his navel and foot.\n\nThe '**golden ratio**' - also known as the divine proportion - has been a phenomenon of interest since ancient times due to its unique mathematical properties and its aesthetic appeal.\n\nOften denoted by the Greek letter phi (Φ or φ), it is approximately equal to 1.618. This means that if you have a line that's 1.618 units long (let's say meters for simplicity), and you divide it so that the longer segment is 1 meter and the shorter segment is 61.8 centimeters, you've divided it according to the golden ratio.\n\n![Graph](image://03d20e91-9b87-4768-8cb6-1a21f8daee17 \"The Golden Ratio Percentage. Image: Public Domain via Wikimedia Commons\")\n\nWhile Leonardo did not explicitly discuss the golden ratio (as far as current evidence suggests), many scholars and enthusiasts believe that he was aware of it and applied it in his works, which would align with his deep interest in the mathematical principles that govern the proportions of the human body.","3a9826e4-51bb-47b3-bef9-df2796268b25",[172],{"id":173,"data":174,"type":53,"version":35,"maxContentLevel":19},"c55a58c3-bd16-4d87-bd3d-d54a76f9963f",{"type":53,"reviewType":19,"spacingBehaviour":35,"multiChoiceQuestion":175,"multiChoiceCorrect":177,"multiChoiceIncorrect":179,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[176],"What is the golden ratio, approximately?",[178],"1.618",[180,181,182],"1.186","1.861","1.681",{"id":184,"data":185,"type":35,"maxContentLevel":19,"version":19,"reviews":188},"932ffc82-6859-4ef7-a433-da920da326ae",{"type":35,"markdownContent":186,"audioMediaId":187},"The golden ratio is related to the 'Fibonacci sequence': a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.\n\n![Graph](image://1b0eb1a8-301e-4d12-b6c4-aa57b3cda5f2 \"Tiled squares representing the Fibonacci sequence. Image: Romain, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons.\")\n\nWhen you take the ratio of successive Fibonacci numbers, you'll notice an interesting phenomenon.\n\nAs you move further along the sequence, the ratio of one number to its preceding number gets closer and closer to the golden ratio. For example: 5/3 = 1.666... 8/5 = 1.60... 21/13 = 1.615... 34/21 = 1.619... The golden ratio and Fibonacci sequence can be found almost everywhere in nature, as well as in the proportions of the human body, and many great works of art and architecture.\n\nA commonly cited example is the nautilus shell, which grows in a logarithmic spiral. If you measure the various dimensions of its coil and their ratio from one chamber to the next, they often approximate the golden ratio.\n\n![Graph](image://38b60192-effb-4576-a380-2e3af3917c17 \"Fibonacci spiral: Image: Public Domain via Wikimedia commons\")","709611fa-b746-4570-9c36-e9d4ae48e94d",[189,196],{"id":190,"data":191,"type":53,"version":35,"maxContentLevel":19},"3c22c024-7440-4dee-b45f-8d23716b9aeb",{"type":53,"reviewType":35,"spacingBehaviour":35,"activeRecallQuestion":192,"activeRecallAnswers":194},[193],"What happens when you take the ratio of successive Fibonacci numbers?",[195],"The ratio gets closer and closer to the golden ratio",{"id":197,"data":198,"type":53,"version":35,"maxContentLevel":19},"d0ff4fdc-783f-47a4-8155-4060b8ef747d",{"type":53,"reviewType":19,"spacingBehaviour":35,"multiChoiceQuestion":199,"multiChoiceCorrect":201,"multiChoiceIncorrect":203,"multiChoiceMultiSelect":6,"multiChoiceRevealAnswerOption":6},[200],"How is the Fibonacci sequence generated?",[202],"Each number is the sum of the two preceding ones",[204,205,206],"Each number is the product of the two preceding ones","Each number is the difference of the two preceding ones","Each number is the square of the preceding one",[208,400],{"id":23,"data":24,"type":25,"version":20,"maxContentLevel":19,"summaryPage":27,"introPage":36,"pages":209},[210,270,305,340,370],{"id":45,"data":46,"type":35,"maxContentLevel":19,"version":25,"reviews":49,"parsed":211},{"data":212,"body":215,"toc":268},{"title":213,"description":214},"","The study of anatomy during the Renaissance was fraught with religious controversy. The Church generally frowned upon the dissection of human bodies, viewing it as a desecration of the sacred human form.",{"type":216,"children":217},"root",[218,225,235,240,245,250,255,263],{"type":219,"tag":220,"props":221,"children":222},"element","p",{},[223],{"type":224,"value":214},"text",{"type":219,"tag":220,"props":226,"children":227},{},[228],{"type":219,"tag":229,"props":230,"children":234},"img",{"alt":231,"src":232,"title":233},"Graph","image://6edd5fd8-fafe-441f-a79b-0a6c5c5386a1","Leonardo's sketch of the major vessels of a human body, showing his interest in anatomy. Image: Public Domain via Wikimedia",[],{"type":219,"tag":220,"props":236,"children":237},{},[238],{"type":224,"value":239},"This prohibition greatly hampered knowledge of anatomy during this time, and acquiring cadavers for research was a taboo often navigated by robbing graves illegally.",{"type":219,"tag":220,"props":241,"children":242},{},[243],{"type":224,"value":244},"So why did da Vinci persevere?",{"type":219,"tag":220,"props":246,"children":247},{},[248],{"type":224,"value":249},"Leonardo’s insatiable curiosity in this area was rooted in his belief in the interconnectedness of art and nature. He saw the human body as a masterpiece of nature's design, a perfect blend of form and function, and sought to understand it in its entirety.",{"type":219,"tag":220,"props":251,"children":252},{},[253],{"type":224,"value":254},"This fascination is visible in the intricate sketches of the human skull that he began drawing in 1489. The skull was one of his very first dissections.",{"type":219,"tag":220,"props":256,"children":257},{},[258],{"type":219,"tag":229,"props":259,"children":262},{"alt":231,"src":260,"title":261},"image://5bb520cf-fb14-47b5-87c9-61cddc205f0d","Da Vinci's sketch of the skull. Image: Leonardo da Vinci via Wikimedia",[],{"type":219,"tag":220,"props":264,"children":265},{},[266],{"type":224,"value":267},"In these early anatomical manuscripts, he depicted the cranium divided into two sections: one showing the exterior with teeth and jaw and the other showing the cavities within them.",{"title":213,"searchDepth":25,"depth":25,"links":269},[],{"id":59,"data":60,"type":35,"maxContentLevel":19,"version":25,"parsed":271},{"data":272,"body":274,"toc":303},{"title":213,"description":273},"Leonardo's anatomical sketches are celebrated for their precision and attention to detail. They also often went beyond static depictions of the human body and often constituted studies of the body in motion.",{"type":216,"children":275},[276,280,285,293,298],{"type":219,"tag":220,"props":277,"children":278},{},[279],{"type":224,"value":273},{"type":219,"tag":220,"props":281,"children":282},{},[283],{"type":224,"value":284},"This reflected da Vinci’s fascination with the unity of form and function.",{"type":219,"tag":220,"props":286,"children":287},{},[288],{"type":219,"tag":229,"props":289,"children":292},{"alt":231,"src":290,"title":291},"image://3c4590f6-de0a-406d-a79b-a8503fa09441","The superficial anatomy of the shoulder and neck. Image: Public Domain via Wikimedia commons",[],{"type":219,"tag":220,"props":294,"children":295},{},[296],{"type":224,"value":297},"In his sketches, Leonardo meticulously displayed the interplay of veins, arteries, muscles, internal organs, and bones. He typically portrayed the body’s intricacies through transparent layers, which afforded an “insight” into the organ through the use of sections in perspective.",{"type":219,"tag":220,"props":299,"children":300},{},[301],{"type":224,"value":302},"Even though his medical investigations remained private and went unpublished during his lifetime, the wealth of Leonardo’s drawings that have survived forged are still considered exemplars of scientific illustration.",{"title":213,"searchDepth":25,"depth":25,"links":304},[],{"id":64,"data":65,"type":35,"maxContentLevel":19,"version":25,"parsed":306},{"data":307,"body":309,"toc":338},{"title":213,"description":308},"Leonardo's detailed studies of the human skeleton, muscles, and internal organs garnered a great deal of valuable insights into the human body. His clever scientific illustration techniques - such as his use of cross-sections, transparent overlays, and perspective - have also stood the test of time.",{"type":216,"children":310},[311,315,320,328,333],{"type":219,"tag":220,"props":312,"children":313},{},[314],{"type":224,"value":308},{"type":219,"tag":220,"props":316,"children":317},{},[318],{"type":224,"value":319},"In terms of medical progress, Leonardo was one of the first people to accurately represent the human spine in all its complexity.",{"type":219,"tag":220,"props":321,"children":322},{},[323],{"type":219,"tag":229,"props":324,"children":327},{"alt":231,"src":325,"title":326},"image://2bde3ab6-fb48-4f15-bc48-1079981c38bb","Leonardo's sketches of joints and skeletal muscle. Image: Tangopaso, Public domain, via Wikimedia Commons",[],{"type":219,"tag":220,"props":329,"children":330},{},[331],{"type":224,"value":332},"Additionally, Leonardo's studies of the heart were so advanced that they prefigured modern cardiology.",{"type":219,"tag":220,"props":334,"children":335},{},[336],{"type":224,"value":337},"His understanding of the heart's structure and function, as depicted in his sketches, was far ahead of his time. For example, he was aware of the four chambers of the heart, the existence of heart valves, and the important idea of coronary circulation.",{"title":213,"searchDepth":25,"depth":25,"links":339},[],{"id":69,"data":70,"type":35,"maxContentLevel":19,"version":20,"reviews":73,"parsed":341},{"data":342,"body":344,"toc":368},{"title":213,"description":343},"One of Leonardo's most famous anatomical works is titled 'Studies of the Fetus in the Womb'. These two colored and annotated sketches were made around 1511 and provide a staggeringly detailed depiction of a fetus in utero.",{"type":216,"children":345},[346,350,358,363],{"type":219,"tag":220,"props":347,"children":348},{},[349],{"type":224,"value":343},{"type":219,"tag":220,"props":351,"children":352},{},[353],{"type":219,"tag":229,"props":354,"children":357},{"alt":231,"src":355,"title":356},"image://57768032-fbd2-43fb-86c9-4a8fa98f3f6e","Leonardo da Vinci's Studies of the Foetus in the Womb. Image: Leonardo da Vinci, Public domain, via Wikimedia Commons.",[],{"type":219,"tag":220,"props":359,"children":360},{},[361],{"type":224,"value":362},"These sketches showcase Leonardo's innovative use of cross-sections and multiple perspectives - techniques he used to represent the complex structure of the dissected womb and the correctly positioned fetus within it.",{"type":219,"tag":220,"props":364,"children":365},{},[366],{"type":224,"value":367},"Leonardo accurately depicted the uterus as having a single chamber. This was in contrast to the prevailing belief that it had multiple chambers that divided fetuses into separate compartments in the case of twins!",{"title":213,"searchDepth":25,"depth":25,"links":369},[],{"id":82,"data":83,"type":35,"maxContentLevel":19,"version":25,"reviews":86,"parsed":371},{"data":372,"body":374,"toc":398},{"title":213,"description":373},"Leonardo's anatomical studies enabled him to depict the human form with unparalleled realism and accuracy. His enriched understanding of both the structure and function of the human body, allowed him to confidently portray human figures in an array of expressive poses and actions, capturing the subtleties of movement and posture.",{"type":216,"children":375},[376,380,385,393],{"type":219,"tag":220,"props":377,"children":378},{},[379],{"type":224,"value":373},{"type":219,"tag":220,"props":381,"children":382},{},[383],{"type":224,"value":384},"His understanding of facial muscles and their connections also made da Vinci skilled in conveying emotions, making ready use of the play of light and shadow over muscles, and bones.",{"type":219,"tag":220,"props":386,"children":387},{},[388],{"type":219,"tag":229,"props":389,"children":392},{"alt":231,"src":390,"title":391},"image://6a91cc70-4252-4ee7-a103-f5c6d8ed92cc","Head and shoulders of a man, seen from the left, showing the muscles of the neck, chest and shoulder. Etching by Wenceslaus Hollar after Leonardo da Vinci, 1651. Image: Wellcome Collection, CC BY 4.0 \u003Chttps://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons. ",[],{"type":219,"tag":220,"props":394,"children":395},{},[396],{"type":224,"value":397},"Combined with his skilled representation of the texture and surface of the skin, this anatomical realism adds beautiful depth to the faces in da Vinci’s paintings.",{"title":213,"searchDepth":25,"depth":25,"links":399},[],{"id":95,"data":96,"type":25,"version":19,"maxContentLevel":19,"summaryPage":98,"introPage":106,"pages":401},[402,463,506,556],{"id":114,"data":115,"type":35,"maxContentLevel":19,"version":19,"reviews":118,"parsed":403},{"data":404,"body":406,"toc":461},{"title":213,"description":405},"The study of human proportion wasn’t a new concept. The ancient Greeks and Romans also studied the human form in great detail, producing some of the most accurate sculptures that remain to this day.",{"type":216,"children":407},[408,412,417,422,430,438,443,448,456],{"type":219,"tag":220,"props":409,"children":410},{},[411],{"type":224,"value":405},{"type":219,"tag":220,"props":413,"children":414},{},[415],{"type":224,"value":416},"However, during the Renaissance, these studies took on a new lease of life, as the human form was believed to reflect the divine perfection of the universe, as created by God.",{"type":219,"tag":220,"props":418,"children":419},{},[420],{"type":224,"value":421},"Prominent artists such as Albrecht Dürer conducted extensive studies on human proportions, aiming to discover a mathematical and aesthetic ideal.",{"type":219,"tag":220,"props":423,"children":424},{},[425],{"type":219,"tag":229,"props":426,"children":429},{"alt":231,"src":427,"title":428},"image://a028e2fe-0633-42cd-a87d-ac1e1084dac5","A portrait of Albrecht Dürer. Image: Public Domain via Wikimedia",[],{"type":219,"tag":220,"props":431,"children":432},{},[433],{"type":219,"tag":229,"props":434,"children":437},{"alt":231,"src":435,"title":436},"image://a48a278a-7d09-4ac9-91da-e9c921797e8b","A page from Four Books on Human Proportion. Image: Metropolitan Museum of Art, CC0 \t\nhttps://creativecommons.org/publicdomain/zero/1.0/ via Wikimedia commons.",[],{"type":219,"tag":220,"props":439,"children":440},{},[441],{"type":224,"value":442},"By far the most famous product of the study of human proportion during the Renaissance is the 'Vitruvian Man', a drawing by Leonardo.",{"type":219,"tag":220,"props":444,"children":445},{},[446],{"type":224,"value":447},"It’s a work that is widely considered to be among the all-time most iconic images in Western civilization.",{"type":219,"tag":220,"props":449,"children":450},{},[451],{"type":219,"tag":229,"props":452,"children":455},{"alt":231,"src":453,"title":454},"image://a9274ed9-ca4f-4613-89bf-12812baa71b5","The Vitruvian Man by Leonardo da Vinci. Image: Public Domain via Wikimedia",[],{"type":219,"tag":220,"props":457,"children":458},{},[459],{"type":224,"value":460},"It’s dated to around 1490 and depicts a nude man in two superimposed positions with his arms and legs apart, inscribed in a circle and square. It is an attempt to represent the mathematical principles that govern the proportions of the human body.",{"title":213,"searchDepth":25,"depth":25,"links":462},[],{"id":134,"data":135,"type":35,"maxContentLevel":19,"version":25,"reviews":138,"parsed":464},{"data":465,"body":467,"toc":504},{"title":213,"description":466},"The drawing of the 'Vitruvian Man' was named after the ancient Roman architect Vitruvius, who lived during the 1st century BC. Vitruvius is best known for his multi-volume treatise titled De Architectura.",{"type":216,"children":468},[469,481,486,494,499],{"type":219,"tag":220,"props":470,"children":471},{},[472,474,479],{"type":224,"value":473},"The drawing of the 'Vitruvian Man' was named after the ancient Roman architect Vitruvius, who lived during the 1st century BC. Vitruvius is best known for his multi-volume treatise titled ",{"type":219,"tag":475,"props":476,"children":477},"em",{},[478],{"type":224,"value":165},{"type":224,"value":480},".",{"type":219,"tag":220,"props":482,"children":483},{},[484],{"type":224,"value":485},"This treatise, which is the only treatise on architecture to have survived from antiquity, outlined his principles governing Greek and Roman buildings, as well as the ideal proportions of the human body.",{"type":219,"tag":220,"props":487,"children":488},{},[489],{"type":219,"tag":229,"props":490,"children":493},{"alt":231,"src":491,"title":492},"image://91e742c3-36c8-4800-9cfb-0db05ba5fa88","Italian translation of De Architectura. Image: Metropolitan Museum of Art, CC0 \t\nhttps://creativecommons.org/publicdomain/zero/1.0/ via Wikimedia commons.",[],{"type":219,"tag":220,"props":495,"children":496},{},[497],{"type":224,"value":498},"Little is known with certainty about Vitruvius’ life, but his discussion of perfect proportion in architecture and the human body directly inspired Leonardo’s sketch.",{"type":219,"tag":220,"props":500,"children":501},{},[502],{"type":224,"value":503},"Leonardo was a great admirer of Vitruvius, and he sought to visually represent the architect's concept of the proportionally ideal human body in his drawing.",{"title":213,"searchDepth":25,"depth":25,"links":505},[],{"id":167,"data":168,"type":35,"maxContentLevel":19,"version":19,"reviews":171,"parsed":507},{"data":508,"body":510,"toc":554},{"title":213,"description":509},"The Vitruvian Man is known for exhibiting what’s known as the 'golden ratio' in the man's height relative to the distance between his navel and foot.",{"type":216,"children":511},[512,525,536,541,549],{"type":219,"tag":220,"props":513,"children":514},{},[515,517,523],{"type":224,"value":516},"The Vitruvian Man is known for exhibiting what’s known as the '",{"type":219,"tag":518,"props":519,"children":520},"strong",{},[521],{"type":224,"value":522},"golden ratio",{"type":224,"value":524},"' in the man's height relative to the distance between his navel and foot.",{"type":219,"tag":220,"props":526,"children":527},{},[528,530,534],{"type":224,"value":529},"The '",{"type":219,"tag":518,"props":531,"children":532},{},[533],{"type":224,"value":522},{"type":224,"value":535},"' - also known as the divine proportion - has been a phenomenon of interest since ancient times due to its unique mathematical properties and its aesthetic appeal.",{"type":219,"tag":220,"props":537,"children":538},{},[539],{"type":224,"value":540},"Often denoted by the Greek letter phi (Φ or φ), it is approximately equal to 1.618. This means that if you have a line that's 1.618 units long (let's say meters for simplicity), and you divide it so that the longer segment is 1 meter and the shorter segment is 61.8 centimeters, you've divided it according to the golden ratio.",{"type":219,"tag":220,"props":542,"children":543},{},[544],{"type":219,"tag":229,"props":545,"children":548},{"alt":231,"src":546,"title":547},"image://03d20e91-9b87-4768-8cb6-1a21f8daee17","The Golden Ratio Percentage. Image: Public Domain via Wikimedia Commons",[],{"type":219,"tag":220,"props":550,"children":551},{},[552],{"type":224,"value":553},"While Leonardo did not explicitly discuss the golden ratio (as far as current evidence suggests), many scholars and enthusiasts believe that he was aware of it and applied it in his works, which would align with his deep interest in the mathematical principles that govern the proportions of the human body.",{"title":213,"searchDepth":25,"depth":25,"links":555},[],{"id":184,"data":185,"type":35,"maxContentLevel":19,"version":19,"reviews":188,"parsed":557},{"data":558,"body":560,"toc":597},{"title":213,"description":559},"The golden ratio is related to the 'Fibonacci sequence': a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.",{"type":216,"children":561},[562,566,574,579,584,589],{"type":219,"tag":220,"props":563,"children":564},{},[565],{"type":224,"value":559},{"type":219,"tag":220,"props":567,"children":568},{},[569],{"type":219,"tag":229,"props":570,"children":573},{"alt":231,"src":571,"title":572},"image://1b0eb1a8-301e-4d12-b6c4-aa57b3cda5f2","Tiled squares representing the Fibonacci sequence. Image: Romain, CC BY-SA 4.0 \u003Chttps://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons.",[],{"type":219,"tag":220,"props":575,"children":576},{},[577],{"type":224,"value":578},"When you take the ratio of successive Fibonacci numbers, you'll notice an interesting phenomenon.",{"type":219,"tag":220,"props":580,"children":581},{},[582],{"type":224,"value":583},"As you move further along the sequence, the ratio of one number to its preceding number gets closer and closer to the golden ratio. For example: 5/3 = 1.666... 8/5 = 1.60... 21/13 = 1.615... 34/21 = 1.619... The golden ratio and Fibonacci sequence can be found almost everywhere in nature, as well as in the proportions of the human body, and many great works of art and architecture.",{"type":219,"tag":220,"props":585,"children":586},{},[587],{"type":224,"value":588},"A commonly cited example is the nautilus shell, which grows in a logarithmic spiral. If you measure the various dimensions of its coil and their ratio from one chamber to the next, they often approximate the golden ratio.",{"type":219,"tag":220,"props":590,"children":591},{},[592],{"type":219,"tag":229,"props":593,"children":596},{"alt":231,"src":594,"title":595},"image://38b60192-effb-4576-a380-2e3af3917c17","Fibonacci spiral: Image: Public Domain via Wikimedia commons",[],{"title":213,"searchDepth":25,"depth":25,"links":598},[],{"left":4,"top":4,"width":600,"height":600,"rotate":4,"vFlip":6,"hFlip":6,"body":601},24,"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"m9 18l6-6l-6-6\"/>",{"left":4,"top":4,"width":600,"height":600,"rotate":4,"vFlip":6,"hFlip":6,"body":603},"\u003Cpath fill=\"none\" stroke=\"currentColor\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke-width=\"2\" d=\"M4 5h16M4 12h16M4 19h16\"/>",1778179235392]