Leonardo da Vinci used detailed drawings and sketches to explore and develop ideas in which fields of knowledge?

Introduction / Context:
Leonardo da Vinci is one of the most famous polymaths in history. He is remembered not just as an artist, but also as an engineer, inventor, anatomist and thinker. His notebooks contain thousands of drawings that blend artistic talent with scientific curiosity and mathematical observation. This question checks whether you understand that his drawings served as tools across many disciplines, not in art alone.

Given Data / Assumptions:

• The question mentions Leonardo da Vinci and his use of drawings.
• Options list different combinations of fields such as art, science, mathematics, engineering and religious studies.
• We assume basic awareness of Renaissance history and Leonardo’s notebooks.

Concept / Approach:
The concept tested is the idea of a polymath, a person skilled in many different fields. Leonardo’s sketches show studies of human muscles, bones and organs, mechanical devices like gears and flying machines, and precise geometric forms used in his paintings. Therefore, any correct answer must include at least art, science and mathematics together. An option that restricts him to just one or two of these domains does not reflect his wide ranging use of drawing as a thinking tool.

Step-by-Step Solution:
Step 1: Recall that Leonardo painted works like the Mona Lisa and The Last Supper, proving his mastery of art.Step 2: Remember that his notebooks contain anatomical sketches of the human body, showing deep scientific and medical interest.Step 3: Note that he designed machines, weapons and flying devices, which required mechanical thinking and mathematics.Step 4: Examine the options and identify which one includes all of these areas together.Step 5: Option d, which states mathematics, science and art together, is the only one that captures his full use of drawings.

Verification / Alternative check:

Why Other Options Are Wrong:
Art only is wrong because it ignores his contributions to anatomy, engineering and scientific observation.Science and human anatomy only is incomplete, since it leaves out his core identity as an artist.Mathematics and engineering only is also incomplete and ignores his artistic masterpieces.Religious studies and philosophy only is incorrect, as there is no major historical tradition that defines Leonardo primarily in those terms.

Common Pitfalls:
A common mistake is to think of Leonardo only as a painter because his artworks are widely reproduced. Another pitfall is focusing only on his flying machine designs and thinking of him only as an engineer. To answer such questions accurately, always recall that he represents the Renaissance ideal of a many sided genius, equally at home in art, science and mathematical thinking.

Final Answer:
The correct answer is Mathematics, science and art together.