Old Proofs to Know (1 Viewer)

[goodcat911]

What are some good old proofs to know that have been or could be used in the hsc previously? I know about some of them like Basel's formula, Wilson's theorem, Squeeze theorem and crap but anyone got a list or smth of interesting ones to know (that are not too crazy)?

 

[Average Boreduser]

APollonius theorem (just convert the triangle into vectors and ur golden)

 

[kendricklamarlover101]

probably nice to know the proof of the triangle inequality and the reverse triangle inequality

 

[Average Boreduser]

probably nice to know the proof of the triangle inequality and the reverse triangle inequality

tbf tho its literally just a geometric proof/ diagram. Nothing rlly to memorise except the vectors.

 

[kendricklamarlover101]

tbf tho its literally just a geometric proof/ diagram. Nothing rlly to memorise except the vectors.

nah ive seen an algebraic proof of it in a paper before and got stuck on the reverse triangle inequality

 

[Average Boreduser]

nah ive seen an algebraic proof of it in a paper before and got stuck on the reverse triangle inequality

Oh fr? Damn lol mbmb

 

[goodcat911]

Apollonius Theorem
Basel’s Problem
Wilson’s Theorem
Squeeze Theorem
De Moivre’s Theorem
King’s Theorem
Triangle Inequality
Taylor Series
Heron’s Formula
Wallis Product
Fermat’s Theorem
Cauchy-Schwarz Inequality
Bayes’ Theorem
Euler’s Formula
Jensen’s Inequality
Thales’s Theorem
Fourier Series
Binomial Theorem
Nesbitt’s Inequality
Circle Geometry Theorems:
- Alternate segment
- Angle at the centre
- Angles in the same segment
- Angles in a semicircle
- Chord of a circle
- Cyclic quadrilateral
- Tangent of a circle
Bolzano-Weierstrass Theorem
Double Induction Principle
Forward-Backward Induction
Euler-Maclaurin Inequality

Anything else?

 

[Average Boreduser]

Apollonius Theorem
Basel’s Problem
Wilson’s Theorem
Squeeze Theorem
De Moivre’s Theorem
King’s Theorem
Triangle Inequality
Taylor Series
Heron’s Formula
Wallis Product
Fermat’s Theorem
Cauchy-Schwarz Inequality
Bayes’ Theorem
Euler’s Formula Proof
Jensen’s Inequality
Thales’s Theorem
Fourier Series
Binomial Theorem
Nesbitt’s Inequality

Anything else?

Probs rlly useful knowing ur circle geo proofs for complex loci. The shit you can do to on that topic is acc crazy.

 

[goodcat911]

Probs rlly useful knowing ur circle geo proofs for complex loci. The shit you can do to on that topic is acc crazy.

ohh yea thx

 

[C_master]

Apollonius Theorem
Basel’s Problem
Wilson’s Theorem
Squeeze Theorem
De Moivre’s Theorem
King’s Theorem
Triangle Inequality
Taylor Series
Heron’s Formula
Wallis Product
Fermat’s Theorem
Cauchy-Schwarz Inequality
Bayes’ Theorem
Euler’s Formula Proof
Jensen’s Inequality
Thales’s Theorem
Fourier Series
Binomial Theorem
Nesbitt’s Inequality
Circle Geometry Theorems:
- Alternate segment
- Angle at the centre
- Angles in the same segment
- Angles in a semicircle
- Chord of a circle
- Cyclic quadrilateral
- Tangent of a circle

Anything else?

The circle geometry theorems are still taught even though it was removed from the syllabus

 

[Average Boreduser]

Another suggestion. Learn the coordinate geo topic. Trust me you’ll thank me when u do ur hscs.

 

[cossine]

Apollonius Theorem
Basel’s Problem
Wilson’s Theorem
Squeeze Theorem
De Moivre’s Theorem
King’s Theorem
Triangle Inequality
Taylor Series
Heron’s Formula
Wallis Product
Fermat’s Theorem
Cauchy-Schwarz Inequality
Bayes’ Theorem
Euler’s Formula
Jensen’s Inequality
Thales’s Theorem
Fourier Series
Binomial Theorem
Nesbitt’s Inequality
Circle Geometry Theorems:
- Alternate segment
- Angle at the centre
- Angles in the same segment
- Angles in a semicircle
- Chord of a circle
- Cyclic quadrilateral
- Tangent of a circle
Bolzano-Weierstrass Theorem

Anything else?

I highly doubt they will appear and be useful but:

double mathematical induction (There is some YouTube author)
forward-back mathematical induction
Euler-Maclaurin Inequality (Keith Conrad has an interesting paper on his website)

On another note If you have time it may be fun to look at the SOME 1/2/3 (Summer of Math Exposition) playlist from 3blue1brown.

 

[Average Boreduser]

Apollonius Theorem
Basel’s Problem
Wilson’s Theorem
Squeeze Theorem
De Moivre’s Theorem
King’s Theorem
Triangle Inequality
Taylor Series
Heron’s Formula
Wallis Product
Fermat’s Theorem
Cauchy-Schwarz Inequality
Bayes’ Theorem
Euler’s Formula
Jensen’s Inequality
Thales’s Theorem
Fourier Series
Binomial Theorem
Nesbitt’s Inequality
Circle Geometry Theorems:
- Alternate segment
- Angle at the centre
- Angles in the same segment
- Angles in a semicircle
- Chord of a circle
- Cyclic quadrilateral
- Tangent of a circle
Bolzano-Weierstrass Theorem
Double Induction Principle
Forward-Backward Induction
Euler-Maclaurin Inequality

Anything else?

One thing taht could also be useful is a the angle subtended by an arc in a circle is /2 from the arc to the center coordinate (if that makes sense)

<POQ=2*<PAQ

sometimes helpful when sketching loci in cmplx