Self-learner path.

[King Friday]

I'm studying Algebra 1 & 2 right now and I enjoy it.
I'm then going to take High School Geometry.
Am I on the right learning path to eventually learn Calculus to a respectable level?

Thank you in advance!
KF

 

[blamocur]

Geometry is an interesting subject by itself, but I do't think it is a prerequisite for learning calculus.

 

[fresh_42]

Geometry is an interesting subject by itself, but I do't think it is a prerequisite for learning calculus.

If you see it as a collection of problems drawn by a compass and a ruler, then maybe not. But quite a few theorems anf formulas are really helpful and should be in the repertoire:

• Thales's theorem
• Cosine theorem with Pythagoras as a special case
• Sum of angles in a polygon
• Trigonometric functions
• Catenary
• Right triangles
• Area and volume formulas
• Perpendiculars
• Golden ratio

You don't need to know how to construct a heptadecagon, but knowing how to deal with the cosine function is definitely an advantage.

 

[King Friday]

If you see it as a collection of problems drawn by a compass and a ruler, then maybe not. But quite a few theorems anf formulas are really helpful and should be in the repertoire:

• Thales's theorem
• Cosine theorem with Pythagoras as a special case
• Sum of angles in a polygon
• Trigonometric functions
• Catenary
• Right triangles
• Area and volume formulas
• Perpendiculars
• Golden ratio

You don't need to know how to construct a heptadecagon, but knowing how to deal with the cosine function is definitely an advantage.

I am, at my level unfamiliar with most of these terms.
But I have repeatedly read that it's a fundamental part of prep for Calculus.
On Udemy, I'm taking this course next:

Master Geometry: Full Curriculum with Practice​

 

[blamocur]

Familiarity with trigonometric functions, as well as with some other functions (exponents, logarithms, hyperbolic functions), and their properties is a good idea because they are used in calculus, but I am not sure that those belong in geometry.

 

[King Friday]

Familiarity with trigonometric functions, as well as with some other functions (exponents, logarithms, hyperbolic functions), and their properties is a good idea because they are used in calculus, but I am not sure that those belong in geometry.

They don't.

 

[fresh_42]

Familiarity with trigonometric functions, as well as with some other functions (exponents, logarithms, hyperbolic functions), and their properties is a good idea because they are used in calculus, but I am not sure that those belong in geometry.

[imath] \dfrac{\text{adjacent}}{\text{hypotenuse}} [/imath] shouldn't be geometry?

Everything that comes with right angles is important, and even more so in complex calculus. Geometry means measuring lengths and angles. On the other side, calculus is heavily dependent on the Euclidean (sic!) metric. It may not be visible throughout calculus, but it is as basic as arithmetic is.

 

[fresh_42]

They don't.

They do.

 

[khansaheb]

Am I on the right learning path to eventually learn Calculus to a respectable level?

That answer depends on the answer of this following question:

What do you want to do with the "learning"?

If you want to follow through by

applying your knowledge of calculus to some "practical field" (like - engineering, astronomy, etc.).

If want to excel in engineering problem solving - Knowledge of geometry is extremely useful - almost essential.

So

What do you want to do after your Calculus journey?

 

[fresh_42]

I agree with @khansaheb. To study something always depends on the answer to the question "what for?" It is one thing to help kids with their homework assignments, or to want to understand the proof of FLT, or to study the various proposals for a GUT. And it is again something different to study mathematics for entertainment or fun.

 

[blamocur]

That answer depends on the answer of this following question:

What do you want to do with the "learning"?

If you want to follow through by

applying your knowledge of calculus to some "practical field" (like - engineering, astronomy, etc.).

If want to excel in engineering problem solving - Knowledge of geometry is extremely useful - almost essential.

So

What do you want to do after your Calculus journey?

I've spent decades working as an engineer, mostly in the fields requiring math (signal, image and video processing, machine vision and communications). I don't remember using classical geometry (Pythagoras theorem is the only exception which comes to mind), but mostly calculus, linear algebra, abstract algebra (finite fields), probability and trigonometry.

Having said that, classical geometry is an elegant field, and I'd be the last person to discourage someone from studying it for fun and for exercising one's brain.

 

[King Friday]

I've spent decades working as an engineer, mostly in the fields requiring math (signal, image and video processing, machine vision and communications). I don't remember using classical geometry (Pythagoras theorem is the only exception which comes to mind), but mostly calculus, linear algebra, abstract algebra (finite fields), probability and trigonometry.

Having said that, classical geometry is an elegant field, and I'd be the last person to discourage someone from studying it for fun and for exercising one's brain.

Thanks for the reply especially from a working engineer!
I've just read so many articles/blogs that Geometry plays a role in calculus, which is preceded by Trigonometry, which is very dependent on Geometry, is it not?

 

[blamocur]

Thanks for the reply especially from a working engineer!
I've just read so many articles/blogs that Geometry plays a role in calculus, which is preceded by Trigonometry, which is very dependent on Geometry, is it not?

Besides Pythagoras I haven't noticed much dependency, sorry. But I'd be interested to hear about counterexamples.

 

[fresh_42]

I've spent decades working as an engineer, mostly in the fields requiring math (signal, image and video processing, machine vision and communications).

Isn't mechanical engineering full of classical geometry? I cannot imagine building a bridge and calculating the static without it.

 

[blamocur]

Isn't mechanical engineering full of classical geometry? I cannot imagine building a bridge and calculating the static without it.

I'd expect linear algebra and trigonometry there. Well, some trigonometric properties of triangles might be helpful, but together with Pythagoras this is a small part of geometry, isn't it?

 

[fresh_42]

It all depends on the range of what one would consider geometry. I think that any definition or theorem around right angles is important. From there to arbitrary triangles is a small step. The German word for centroid is basically mass center. This already indicates the importance of that point. As I already mentioned, we don't need to know how to build a heptadecagon with a compass and a ruler, and many more theorems may not be particularly helpful, but I think the basics are as important as arithmetic is. I cannot draw a square root by hand anymore, but I'm happy that I can calculate with fractions. The same is true for geometry in my mind. Knowing Thales is simply an advantage in several places. And, of course, it all depends on the central question of "what for". I could imagine that even hobby astronomy is hard without basic skills in geometry.

 

[King Friday]

It all depends on the range of what one would consider geometry. I think that any definition or theorem around right angles is important. From there to arbitrary triangles is a small step. The German word for centroid is basically mass center. This already indicates the importance of that point. As I already mentioned, we don't need to know how to build a heptadecagon with a compass and a ruler, and many more theorems may not be particularly helpful, but I think the basics are as important as arithmetic is. I cannot draw a square root by hand anymore, but I'm happy that I can calculate with fractions. The same is true for geometry in my mind. Knowing Thales is simply an advantage in several places. And, of course, it all depends on the central question of "what for". I could imagine that even hobby astronomy is hard without basic skills in geometry.

Which is why I think High School level geometry will lend itself to use in Trigonometry and thus to Calculus. This is my understanding having not gone that far myself, all I can do is make connections.

 

[jonah2.0]

Beer induced query follows.

I'm studying Algebra 1 & 2 right now and I enjoy it.
I'm then going to take High School Geometry.
Am I on the right learning path to eventually learn Calculus to a respectable level?

Thank you in advance!
KF

Algebra 1 & 2?
Studying it as in a High School setting or as in reviewing/studying it on your own?
Not too clear on your declaration.
Needs clarification.

 

[The Highlander]

Beer induced query follows.

Algebra 1 & 2?
Studying it as in a High School setting or as in reviewing/studying it on your own?
Not too clear on your declaration.
Needs clarification.

The OP mentions here that s/he is 68 years old; I expect that probably narrows down the options.

 

[King Friday]

Beer induced query follows.

Algebra 1 & 2?
Studying it as in a High School setting or as in reviewing/studying it on your own?
Not too clear on your declaration.
Needs clarification.

I am 68 years old and studying high school Algebra at home with an online course on Udemy.
My hope is a progress to Pre-Calc and eventually Calculus. I was inquiring about the best course choice to achieve that goal.
Not sure how to put it any more plainly.
Currently I am about 2/3 of the way through Algebra 1 after about a week.
After Algebra 1, I was thinking about High School Geometry as it ties into Trigonometry, which is a part of Pre-Calculus.
At least that's my understanding of it.