Euclidean Geometry reading respond.
Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?
Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful?
For over 2,000 years, Euclid ’s works were considered the explicit textbooks not only for geometry, but also for the absoluteness of mathematics. Even in modern times, several influential scholars have been sparked by the beauty of the work. Hobbes, Einstein, and Russell all praised the work–not only for its mathematical accuracy of geometry, number theory, and ancient algebra, but also for its beauty and power to show these infinite, pre-existing facts to the eye of mankind.
We may have realized that the ancients and early moderns saw mathematics differently. Plato, Euclid saw mathematics as much more than a set of tools for solving practical problems. These men believed that the beauty and clarity of mathematics emphasized its importance and power. For Plato and Euclid, this meant that the study of mathematics moved one beyond the world of the material and into the more pure planet of the Forms.[1]
Euclidean Geometry is a difficult discipline that takes serious study, mental sharpness, and transparency of thinking and expression. Geometry proofs can sharpen the minds. The reasoning must used for each steps, and each claim must logically follow from those already definitively demonstrated. Errors are uncovered instantly in geometry. Geometry organizes the mind to think on truths that do not expire. These truths are eternal. These truths are sure. These truths are foundational in the very element of the world.
Next time the students ask, “Why do I need to learn this math I’ll never use?” answer, “Because it helps you participate in the good, true, beautiful, eternal, and never changing divine thoughts of God. Studying this rigorous discipline will train your mind to think on higher thoughts and prepare it for the spiritual ascent to participation in the divine nature.”[2]
[1] GLENN MORRROW, INTRODUCTION TO PROCLUS, A COMMENTARY ON THE FIRST BOOK OF EUCLID’S ELEMENTS, TRANS. GLENN R. MORROW (PRINCETON: PRINCETON UNIVERSITY PRESS, 1992), XXX. CONSIDERING EUCLID’S CONTEXT, IT SEEMS SAFE TO ASSUME THAT EUCLID HAD PLATONIC LEANINGS. IT IS HARD TO KNOW FOR SURE, BUT A TRADITIONAL UNDERSTANDING OF EUCLID ASSERTS THIS SENTIMENT.
[2] http://adorans.org/?article=the-value-of-euclids-elements
Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?
Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful?
For over 2,000 years, Euclid ’s works were considered the explicit textbooks not only for geometry, but also for the absoluteness of mathematics. Even in modern times, several influential scholars have been sparked by the beauty of the work. Hobbes, Einstein, and Russell all praised the work–not only for its mathematical accuracy of geometry, number theory, and ancient algebra, but also for its beauty and power to show these infinite, pre-existing facts to the eye of mankind.
We may have realized that the ancients and early moderns saw mathematics differently. Plato, Euclid saw mathematics as much more than a set of tools for solving practical problems. These men believed that the beauty and clarity of mathematics emphasized its importance and power. For Plato and Euclid, this meant that the study of mathematics moved one beyond the world of the material and into the more pure planet of the Forms.[1]
Euclidean Geometry is a difficult discipline that takes serious study, mental sharpness, and transparency of thinking and expression. Geometry proofs can sharpen the minds. The reasoning must used for each steps, and each claim must logically follow from those already definitively demonstrated. Errors are uncovered instantly in geometry. Geometry organizes the mind to think on truths that do not expire. These truths are eternal. These truths are sure. These truths are foundational in the very element of the world.
Next time the students ask, “Why do I need to learn this math I’ll never use?” answer, “Because it helps you participate in the good, true, beautiful, eternal, and never changing divine thoughts of God. Studying this rigorous discipline will train your mind to think on higher thoughts and prepare it for the spiritual ascent to participation in the divine nature.”[2]
[1] GLENN MORRROW, INTRODUCTION TO PROCLUS, A COMMENTARY ON THE FIRST BOOK OF EUCLID’S ELEMENTS, TRANS. GLENN R. MORROW (PRINCETON: PRINCETON UNIVERSITY PRESS, 1992), XXX. CONSIDERING EUCLID’S CONTEXT, IT SEEMS SAFE TO ASSUME THAT EUCLID HAD PLATONIC LEANINGS. IT IS HARD TO KNOW FOR SURE, BUT A TRADITIONAL UNDERSTANDING OF EUCLID ASSERTS THIS SENTIMENT.
[2] http://adorans.org/?article=the-value-of-euclids-elements
Wow! Deeply thoughtful and well-researched commentary, Roya! (Would you be willing to share these ideas with the class?)
ReplyDeleteThank you Susan, It would be my pleasure
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