User hyperpallium

36 votes

13 answers

7k views

A way to directly see that the interior angles of triangle sum to $180^\circ$?

geometry visualization

asked Apr 8, 2018 at 12:35

3 votes

2 answers

933 views

A way to directly see the Inscribed angle theorem? (i.e. central angle is twice the inscribed angle)

geometry visualization

asked Apr 12, 2018 at 4:20

3 votes

2 answers

785 views

$f(a) = 0 \implies (x-a) \mid f(x)$? (polynomial zeros imply factors)

algebra-precalculus polynomials

asked May 6, 2018 at 10:20

3 votes

1 answer

254 views

Fundamental Theorem of Algebra proof, for max real roots of real polynomials - using only high school algebra-precalc?

algebra-precalculus polynomials roots

asked May 14, 2018 at 4:17

3 votes

2 answers

1k views

Seeing why horizontal shifts are reversed?

algebra-precalculus graphing-functions

asked Jun 9, 2018 at 5:02

3 votes

2 answers

520 views

prove $x+y=a, xy=b$ uniquely determine $x,y$

algebra-precalculus proof-verification proof-writing

asked Aug 13, 2018 at 7:34

3 votes

1 answer

131 views

Are there other self-similar functions like $e^x$ and $\cos x$? [duplicate]

algebra-precalculus ordinary-differential-equations derivatives

asked Sep 16, 2018 at 1:21

3 votes

3 answers

672 views

Technique for simplifying, e.g. $\sqrt{ 8 - 4\sqrt{3}}$ to $\sqrt{6} - \sqrt{2}$

algebra-precalculus radicals

asked May 24, 2020 at 5:25

2 votes

1 answer

406 views

Is there a term analogous to factoring, for addition?

soft-question terminology arithmetic

asked Jun 8, 2018 at 6:28

2 votes

3 answers

490 views

When can one apply limit properties?

calculus limits

asked Dec 6, 2017 at 6:51

2 votes

5 answers

263 views

Why does subtraction work over positives and negatives (in $\mathbb{Z}$)?

arithmetic integers

asked Jan 28, 2018 at 2:40

1 vote

1 answer

63 views

For a group [Z,+] with unlabelled integers, what's an algorithm to determine the positive and negative subsets?

group-theory abelian-groups integers

asked Jan 30, 2018 at 7:08

1 vote

2 answers

296 views

How to generalize the mechanism of subtraction, from naturals to negatives? [closed]

algebra-precalculus reference-request foundations

asked Feb 2, 2018 at 1:32

1 vote

2 answers

77 views

Understanding the law of cosines, directly from the formula

trigonometry

asked Mar 22, 2018 at 4:37

1 vote

2 answers

134 views

Why doesn't $\sqrt{ab}=\sqrt{a}\sqrt{b}$ work for $a,b<0$? [duplicate]

algebra-precalculus complex-numbers radicals

asked Jul 3, 2018 at 5:59

1 vote

1 answer

182 views

Does "standard polynomial form" define an ordering of terms of equal order e.g. $xy^2 + x^2y$

algebra-precalculus polynomials terminology

asked Jul 30, 2018 at 3:44

1 vote

3 answers

210 views

Visual proof of isosceles base-angle congruency?

geometry triangles alternative-proof visualization

asked May 13, 2018 at 4:38

0 votes

0 answers

225 views

If two polynomials over integers are equivalent, are the same polynomial expressions defined over positive integers also equivalent?

proof-verification polynomials

asked Jun 6, 2018 at 9:52

0 votes

0 answers

59 views

Is there a problem with canonical forms for ratios?

ratio

asked Feb 16, 2018 at 4:31

0 votes

1 answer

159 views

A more direct way to see that the angle inscribed in a semicircle is $90^\circ$?

geometry visualization

asked Apr 15, 2018 at 3:13

0 votes

1 answer

22 views

Simple description/name for 0/1 in second position in binary? (analogous to even/odd for 0/1 in first position)

complex-numbers binary

asked May 2, 2018 at 9:16

0 votes

1 answer

440 views

Polynomial Remainder Theorem seems to use divide by zero

algebra-precalculus polynomials

asked May 6, 2018 at 6:46

0 votes

3 answers

189 views

Can we factor multivariate polynomial $x+xy+y$?

polynomials factoring multivariate-polynomial

asked Aug 23, 2018 at 5:55

0 votes

1 answer

87 views

How to improve at handling the (mild) complexity of high school trig?

algebra-precalculus trigonometry soft-question self-learning

asked Apr 7, 2019 at 6:49

0 votes

1 answer

36 views

How to think about/what is the justification for $\pm \sqrt{x^2} = x$?

algebra-precalculus

asked May 16, 2019 at 7:50

0 votes

2 answers

291 views

Algebraic proof that $ ||\vec{a} +\vec{b}|| \le ||\vec{a}|| + ||\vec{b}|| $ [duplicate]

algebra-precalculus

asked Oct 4, 2019 at 3:31

0 votes

1 answer

52 views

Is there a way to directly see the number of combinations? (other than as $n\mathrm{C}r = n\mathrm{P}r/n!$)

algebra-precalculus combinations visualization

asked Dec 11, 2019 at 2:23

0 votes

0 answers

99 views

A way to directly see $a^2+b^2=f^2$ for hyperbolae?

geometry algebra-precalculus conic-sections visualization

asked Dec 24, 2019 at 4:56

-2 votes

1 answer

179 views

Are there number systems that fix divide-by-zero? [duplicate]

algebra-precalculus foundations

asked Oct 18, 2018 at 6:42

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29 Questions

A way to directly see that the interior angles of triangle sum to $180^\circ$?

A way to directly see the Inscribed angle theorem? (i.e. central angle is twice the inscribed angle)

$f(a) = 0 \implies (x-a) \mid f(x)$? (polynomial zeros imply factors)

Fundamental Theorem of Algebra proof, for max real roots of real polynomials - using only high school algebra-precalc?

Seeing why horizontal shifts are reversed?

prove $x+y=a, xy=b$ uniquely determine $x,y$

Are there other self-similar functions like $e^x$ and $\cos x$? [duplicate]

Technique for simplifying, e.g. $\sqrt{ 8 - 4\sqrt{3}}$ to $\sqrt{6} - \sqrt{2}$

Is there a term analogous to factoring, for addition?

When can one apply limit properties?

Why does subtraction work over positives and negatives (in $\mathbb{Z}$)?

For a group [Z,+] with unlabelled integers, what's an algorithm to determine the positive and negative subsets?

How to generalize the mechanism of subtraction, from naturals to negatives? [closed]

Understanding the law of cosines, directly from the formula

Why doesn't $\sqrt{ab}=\sqrt{a}\sqrt{b}$ work for $a,b<0$? [duplicate]

Does "standard polynomial form" define an ordering of terms of equal order e.g. $xy^2 + x^2y$

Visual proof of isosceles base-angle congruency?

If two polynomials over integers are equivalent, are the same polynomial expressions defined over positive integers also equivalent?

Is there a problem with canonical forms for ratios?

A more direct way to see that the angle inscribed in a semicircle is $90^\circ$?

Simple description/name for 0/1 in second position in binary? (analogous to even/odd for 0/1 in first position)

Polynomial Remainder Theorem seems to use divide by zero

Can we factor multivariate polynomial $x+xy+y$?

How to improve at handling the (mild) complexity of high school trig?

How to think about/what is the justification for $\pm \sqrt{x^2} = x$?

Algebraic proof that $ ||\vec{a} +\vec{b}|| \le ||\vec{a}|| + ||\vec{b}|| $ [duplicate]

Is there a way to directly see the number of combinations? (other than as $n\mathrm{C}r = n\mathrm{P}r/n!$)

A way to directly see $a^2+b^2=f^2$ for hyperbolae?

Are there number systems that fix divide-by-zero? [duplicate]