Geometry is based on logic.
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Yes. The geometry taught in today's public schools is based on Euclidian geometry.
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Piccasso Leonardo da Vinci - The Vitruvian man. Based on an ideal human proportion and geometry as described by Vitruvius.
math before was more based off of geometry and math today is more based off of symbols and numbers. though it still contains the focus on geometry within it but not as focused as it is on other expressions.
Intuition, induction, and deduction are types of reasoning used in geometry. Deduction uses logic to form a conclusion based on given statements.