(adsbygoogle = window.adsbygoogle || []).push({}); Should I start with Euclid geometry??

Iam doing electrical engineering course(undergrad first year). I like to see how mathematics works in it's core. From grade 6(when I was 11), when I was introduced algebra, I did my maximum to know how things worked..I would want to know how a particular formula was derived. I made a special attempt to know how pythagoras theorem is proved and so on....I was introduced geometry in grade 7. it appeared like learning straight lines, about different angles(like alternate angle) and so on. A brief overview was given. We had a lot of theorems and proofs on congruency of triangles in grade 8. I just took the theorems on similarity and congruency just for granted(ie..like axioms) and proved many other theorems using it. For grade 9, I had to shift my school where there was a different education board. The students in this board already learnt the axioms on Euclid geometry in grade 8 itself. But they did not have rigorous method of proving. In my new school, we had to prove things like how the the triangle whose one edge is on the circumference of the semicircle and whose another side is the semicircle's diameter is right angled...

We had used the following axioms or theorems like..

1.Area of rectangle is product of length and breadth..

2. Congruency and similarity or triangles.

3.Theorems on angles(like how the measure of vertically opposite angles when two lines are equal).

Though we were presented only this much, I looked these proving exercises as logically conistent and self-contained without going into rigour of euclidean geometry. After few chapters on geometry, we had concept of cartesian co-ordiante system. By using these theorems, I found that we can prove all the formulas like distance-formula, section formula and so on... My book did not mention the proof of Hero's formula but I worked on it for days and proved it myself without using trignometry.

My mind was convinced that I learnt mathematics(except calculus where Iam learning real analysis from Apostol) from scratch but now, I came to know that basic things like congruency and similarity of triangles can be proved by the axioms of Euclid.(from Wikipedia) I saw those axioms and they were simple. I regret of not learning those axioms. This has put my spirits down. My already self-convinced mind is not peaceful now.

Now, should I learn euclid geometry again or am I missing something in not learning it? Is my approach logically incorrect? Please help me...Also help me what to learn(in mathmatics) for logical continuity to convince my mind....

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# Should I start with Euclid geometry?

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