User hyperpallium

8

34

votes

13

answers

5k

views

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

geometry visualization

Jul 18 at 18:39 Michael Hoppe 11.4k

3

votes

1

answer

62

views

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

Sep 16 at 9:56 hyperpallium 462

2

votes

2

answers

92

views

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

algebra-precalculus proof-verification proof-writing

Aug 13 at 8:42 hyperpallium 462

2

votes

1

answer

85

views

Is there a term analogous to factoring, for addition?

soft-question terminology arithmetic

Jun 14 '18 at 7:14 J.-E. Pin 18.8k

1

2

votes

2

answers

234

views

Seeing why horizontal shifts are reversed?

algebra-precalculus graphing-functions

Jun 11 '18 at 11:01 Joe Webster 141

1

2

votes

1

answer

104

views

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

algebra-precalculus polynomials roots

May 14 '18 at 14:18 hyperpallium 462

2

votes

2

answers

290

views

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

algebra-precalculus polynomials

May 10 '18 at 7:52 hyperpallium 462

2

votes

2

answers

382

views

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

geometry visualization

May 8 '18 at 8:10 hyperpallium 462

2

votes

5

answers

202

views

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

arithmetic integers

Feb 20 '18 at 6:24 hyperpallium 462

2

votes

3

answers

96

views

When can one apply limit properties?

calculus limits

Dec 6 '17 at 13:42 Paramanand Singh 52.1k

1

vote

1

answer

39

views

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

algebra-precalculus polynomials terminology

Jul 30 at 5:20 hyperpallium 462

1

vote

2

answers

69

views

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

algebra-precalculus complex-numbers radicals

Jul 3 at 7:22 J.G. 37.7k

2

1

vote

2

answers

274

views

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

algebra-precalculus reference-request foundations

Feb 17 '18 at 3:48 hyperpallium 462

1

vote

1

answer

59

views

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

group-theory abelian-groups integers

Feb 4 '18 at 14:35 Will Orrick 13.8k

0

votes

1

answer

33

views

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

algebra-precalculus

May 16 at 7:53 J.G. 37.7k

0

votes

1

answer

74

views

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

algebra-precalculus trigonometry soft-question self-learning

Apr 11 at 6:14 hyperpallium 462

0

votes

0

answers

33

views

Asymptotic error of forward Euler

convergence numerical-methods taylor-expansion finite-differences

Nov 20 at 9:16 hyperpallium 462

0

votes

0

answers

83

views

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

proof-verification polynomials

Jun 7 '18 at 5:24 hyperpallium 462

0

votes

3

answers

125

views

Visual proof of isosceles base-angle congruency?

geometry triangles alternative-proof visualization

May 21 '18 at 9:28 hyperpallium 462

0

votes

0

answers

53

views

Are Naturals a semiring, Integers a ring, and Rationals a field?

abstract-algebra terminology

May 19 '18 at 3:54 hyperpallium 462

0

votes

1

answer

107

views

Polynomial Remainder Theorem seems to use divide by zero

algebra-precalculus polynomials

May 6 '18 at 10:46 mzg147 329

0

votes

1

answer

19

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

May 3 '18 at 7:28 hyperpallium 462

0

votes

1

answer

124

views

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

geometry visualization

Apr 24 '18 at 6:41 hyperpallium 462

0

votes

2

answers

55

views

Understanding the law of cosines, directly from the formula

trigonometry

Mar 22 '18 at 5:42 hyperpallium 462

0

votes

0

answers

37

views

Is there a problem with canonical forms for ratios?

ratio

Feb 16 '18 at 4:39 hyperpallium 462

-1

votes

3

answers

78

views

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

polynomials factoring multivariate-polynomial

Aug 23 at 13:06 quasi 36.5k

1

-2

votes

1

answer

74

views

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

algebra-precalculus foundations

Oct 18 at 11:23 hyperpallium 462

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27 Questions

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

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

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

Is there a term analogous to factoring, for addition?

Seeing why horizontal shifts are reversed?

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

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

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

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

When can one apply limit properties?

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

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

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

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

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

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

Asymptotic error of forward Euler

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

Visual proof of isosceles base-angle congruency?

Are Naturals a semiring, Integers a ring, and Rationals a field?

Polynomial Remainder Theorem seems to use divide by zero

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

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

Understanding the law of cosines, directly from the formula

Is there a problem with canonical forms for ratios?

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

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