User Circulwyrd

3

14

votes

1

answer

539

views

History of the point at infinity?

math-history projective-geometry

Mar 14 '15 at 13:49 azimut 18.7k

3

8

votes

1

answer

1k

views

equilateral triangle and trisection

geometry

Jun 2 '13 at 17:22 RicardoCruz 3,298

1

7

votes

2

answers

2k

views

Draw three congruent circles all touching one another, and a second set of three such circles, each touching also two of the first set.

inversive-geometry

Jun 23 '14 at 8:10 coproc 1,126

2

6

votes

3

answers

6k

views

Integrating left to right versus right to left.

integration

May 18 '13 at 5:42 Jared 29.2k

5

votes

1

answer

310

views

Show $\sin(x+h) \cdot \cos x - \cos(x+h) \cdot \sin x = \sin h$ (without limits please - straight trigonometry only).

calculus trigonometry

Aug 19 '14 at 18:18 Circulwyrd 1,606

4

votes

1

answer

334

views

'imperfect' numbers

elementary-number-theory perfect-numbers

Jan 3 '20 at 0:42 J. W. Tanner 53.6k

3

4

votes

5

answers

6k

views

Is zero irrational?

soft-question

Jun 28 '19 at 4:32 nmasanta 7,276

1

4

votes

1

answer

572

views

Surface area of platonic solids inscribed in unit sphere.

geometry platonic-solids

Jul 2 '15 at 21:19 Community♦ 1

4

votes

1

answer

412

views

3D Dodecahedron model: Construction question.

geometry polyhedra

May 10 '15 at 16:55 VividD 15.2k

4

votes

1

answer

386

views

Find the circle of inversion that inverts one given triangle into another given triangle.

inversive-geometry

Jul 21 '14 at 15:34 Blue 62.6k

1

3

votes

0

answers

24

views

'Grassmann Algebra' expression for triangle orthocenter.

euclidean-geometry math-history grassmannian

Jan 14 at 20:43 Circulwyrd 1,606

1

3

votes

0

answers

55

views

University math curriculum focused on (or inclusive of) “great historical works” of math?

math-history

Jan 15 '18 at 3:49 Circulwyrd 1,606

1

3

votes

2

answers

772

views

Why is inversion in a straight line the same as reflection?

inversive-geometry

May 28 '14 at 12:57 Circulwyrd 1,606

2

votes

1

answer

84

views

Euclid's Elements book III proposition #31 direct from #20?

euclidean-geometry math-history

Oct 6 '19 at 4:11 Eric Wofsey 259k

1

2

votes

0

answers

77

views

Is this usage of the term 'Jacobian' related to the other uses e.g. matrix or elliptic function?

inversive-geometry

Feb 1 '17 at 15:37 Circulwyrd 1,606

2

votes

0

answers

97

views

(Logic behind) Geometric construction for imaginary roots of quadratic.

euclidean-geometry inversive-geometry

Jan 31 '17 at 19:07 Community♦ 1

2

votes

2

answers

289

views

Another Chinese Remainder Theorem Problem

elementary-number-theory congruences chinese-remainder-theorem

Dec 12 '15 at 23:19 Community♦ 1

2

votes

1

answer

67

views

How to show that $\int_{0}^{\pi}{\sqrt{1 + \cos^2 x}}dx$ not solvable in closed form (or is it?).

calculus

Sep 8 '14 at 13:28 Jack D'Aurizio 327k

1

vote

1

answer

58

views

Decompose the symmetric polynomial $\Sigma{x_1^2x_2^2x_3^2}$ into elementary symmetric polynomials.

abstract-algebra combinatorics symmetric-polynomials

Aug 25 at 20:24 Alien 674

1

vote

0

answers

28

views

synthetic division, use for long division of integers?

math-history

May 7 at 18:52 Circulwyrd 1,606

1

vote

3

answers

52

views

If $A^T = -A$ for an $n \times n$ matrix $A$ with zeros on the diagonal, is the rank at most $n-1$?

linear-algebra

Jan 11 '18 at 3:25 nbubis 30.7k

1

vote

1

answer

73

views

“division algorithm algebra” : supply missing proof from Gauss' Disquisitiones Arithmeticae, article 27

math-history

May 23 '17 at 7:48 Ayesh Bernadge 1

1

vote

1

answer

93

views

Clarify $\lambda - \frac{\lambda(\lambda - 1)}{2!} + \frac{\lambda(\lambda-1)(\lambda-2)}{3!}-\ldots = 1 - (1-1)^\lambda = 1$.

sequences-and-series number-theory

Apr 6 '17 at 16:44 Angelo Rendina 1,763

1

vote

1

answer

428

views

“Outer” Butterfly Theorem

geometry

Oct 25 '16 at 4:41 FerJosafath 1

1

vote

0

answers

24

views

Is $i = \sqrt{1-4x} = 1 - 2x - \sum_{n \geq 2} \frac{2^n \cdot (2n -3)!!}{n!}x^n$ (with $x = \frac{1}{2}$) nonsensical?

convergence-divergence

Oct 20 '15 at 14:27 Community♦ 1

1

vote

0

answers

365

views

Given the circumcircle, the 9-point circle, and the angular measures for a triangle, construct the triangle?

geometry inversive-geometry

Jul 17 '14 at 15:12 Circulwyrd 1,606

1

vote

0

answers

236

views

Why is the “elliptic parallel property” called elliptic?

geometry

Feb 27 '14 at 2:23 Circulwyrd 1,606

1

vote

1

answer

2k

views

A line through the centroid G of $\triangle ABC$ intersects the sides at points X, Y, Z.

geometry

Dec 15 '13 at 0:56 Community♦ 1

1

vote

1

answer

73

views

Antique clock problem: Solve for smallest integer $n \geq0$ in $(h+2n)\bmod {12} = (b + n) \bmod {12},$ where h, b are integers between 12 and 1.

modular-arithmetic

Nov 4 '13 at 0:03 Circulwyrd 1,606

1

vote

1

answer

177

views

Rotation-based solution for constructing equilateral triangle with interior point distant from vertices by 2, 3, and 4 units.

geometry

Oct 2 '13 at 4:14 Calvin Lin 53.1k

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44 Questions

History of the point at infinity?

equilateral triangle and trisection

Draw three congruent circles all touching one another, and a second set of three such circles, each touching also two of the first set.

Integrating left to right versus right to left.

Show $\sin(x+h) \cdot \cos x - \cos(x+h) \cdot \sin x = \sin h$ (without limits please - straight trigonometry only).

'imperfect' numbers

Is zero irrational?

Surface area of platonic solids inscribed in unit sphere.

3D Dodecahedron model: Construction question.

Find the circle of inversion that inverts one given triangle into another given triangle.

'Grassmann Algebra' expression for triangle orthocenter.

University math curriculum focused on (or inclusive of) “great historical works” of math?

Why is inversion in a straight line the same as reflection?

Euclid's Elements book III proposition #31 direct from #20?

Is this usage of the term 'Jacobian' related to the other uses e.g. matrix or elliptic function?

(Logic behind) Geometric construction for imaginary roots of quadratic.

Another Chinese Remainder Theorem Problem

How to show that $\int_{0}^{\pi}{\sqrt{1 + \cos^2 x}}dx$ not solvable in closed form (or is it?).

Decompose the symmetric polynomial $\Sigma{x_1^2x_2^2x_3^2}$ into elementary symmetric polynomials.

synthetic division, use for long division of integers?

If $A^T = -A$ for an $n \times n$ matrix $A$ with zeros on the diagonal, is the rank at most $n-1$?

“division algorithm algebra” : supply missing proof from Gauss' Disquisitiones Arithmeticae, article 27

Clarify $\lambda - \frac{\lambda(\lambda - 1)}{2!} + \frac{\lambda(\lambda-1)(\lambda-2)}{3!}-\ldots = 1 - (1-1)^\lambda = 1$.

“Outer” Butterfly Theorem

Is $i = \sqrt{1-4x} = 1 - 2x - \sum_{n \geq 2} \frac{2^n \cdot (2n -3)!!}{n!}x^n$ (with $x = \frac{1}{2}$) nonsensical?

Given the circumcircle, the 9-point circle, and the angular measures for a triangle, construct the triangle?

Why is the “elliptic parallel property” called elliptic?

A line through the centroid G of $\triangle ABC$ intersects the sides at points X, Y, Z.

Antique clock problem: Solve for smallest integer $n \geq0$ in $(h+2n)\bmod {12} = (b + n) \bmod {12},$ where h, b are integers between 12 and 1.

Rotation-based solution for constructing equilateral triangle with interior point distant from vertices by 2, 3, and 4 units.