Question

How to algebraically prove the sum of the projections of two sides of a triangle is equal to the projection of the third side of the triangle?

score 71 · Answer 1 · 2026-03-28 14:06:32

71

Views

How to algebraically prove the sum of the projections of two sides of a triangle is equal to the projection of the third side of the triangle?

Published on 28 Mar 2026 - 14:06

score 26 · Answer 2 · 2026-03-28 00:00:11

26

Views

Bijective proof for Stirling numbers of the first kind

Published on 28 Mar 2026 - 0:00

score 180 · Answer 3 · 2026-03-26 21:25:46

180

Views

Seeking more alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

Published on 26 Mar 2026 - 21:25

score 39 · Answer 4 · 2026-03-30 13:22:59

39

Views

Prove that $\sum_{k=0}^{n-1}\frac{1}{\prod_{m\neq k}(a_m-a_k)}=0$ for any sequence $a_n$.

Published on 30 Mar 2026 - 13:22

score 106 · Answer 5 · 2026-03-29 22:23:55

106

Views

For $x,y,z$ positive real numbers $3x+4y+7z=1$. Find minumum integer value of $1/x+1/y+1/z$

Published on 29 Mar 2026 - 22:23

score 97 · Answer 6 · 2023-11-29 09:49:52

97

Views

Theorem 3.15 Linear Algebra Friedberg, Insel and Spence how is my counterexample wrong?

Published on 29 Nov 2023 - 9:49

score 84 · Answer 7 · 2023-11-29 18:00:09

84

Views

$\mathbb{R}P^{n-1}$ not a retract of $\mathbb{R}P^n$ via cup product

Published on 29 Nov 2023 - 18:00

score 27 · Answer 8 · 2023-12-01 03:22:24

27

Views

Looking for the name and reference to a table which represents all positive integer numbers

Published on 01 Dec 2023 - 3:22

score 40 · Answer 9 · 2026-04-03 20:34:44

40

Views

How to rigorously prove that if $A\times B\neq\emptyset$ then $(A\times B\subset X\times Y)\iff(A\subset X)\land (B\subset Y)$?

Published on 03 Apr 2026 - 20:34

score 39 · Answer 10 · 2023-12-05 09:17:41

39

Views

Does the equality $\bigcup S(X)=X$ holds for any set $X$?

Published on 05 Dec 2023 - 9:17

score 46 · Answer 11 · 2026-03-28 14:55:06

46

Views

Brezis' exercise 8.28.2: prove that $T$ is a compact operator

Published on 28 Mar 2026 - 14:55

score 79 · Answer 12 · 2026-04-01 14:25:01

79

Views

Is there an alternative proof for $\lim a_n^{\frac{1}{q}}=(\lim a_n)^{\frac1q}$?

Published on 01 Apr 2026 - 14:25

score 51 · Answer 13 · 2026-04-03 03:17:27

51

Views

Easy proof or generalization of a fact about sequences of substructures

Published on 03 Apr 2026 - 3:17

score 85 · Answer 14 · 2023-12-09 12:19:34

85

Views

Evaluating a finite sum.

Published on 09 Dec 2023 - 12:19

score 80 · Answer 15 · 2026-04-01 05:15:55

80

Views

Rotations alternative proofs?

Published on 01 Apr 2026 - 5:15

List Question

How to algebraically prove the sum of the projections of two sides of a triangle is equal to the projection of the third side of the triangle?

Bijective proof for Stirling numbers of the first kind

Seeking more alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

Prove that $\sum_{k=0}^{n-1}\frac{1}{\prod_{m\neq k}(a_m-a_k)}=0$ for any sequence $a_n$.

For $x,y,z$ positive real numbers $3x+4y+7z=1$. Find minumum integer value of $1/x+1/y+1/z$

Theorem 3.15 Linear Algebra Friedberg, Insel and Spence how is my counterexample wrong?

$\mathbb{R}P^{n-1}$ not a retract of $\mathbb{R}P^n$ via cup product

Looking for the name and reference to a table which represents all positive integer numbers

How to rigorously prove that if $A\times B\neq\emptyset$ then $(A\times B\subset X\times Y)\iff(A\subset X)\land (B\subset Y)$?

Does the equality $\bigcup S(X)=X$ holds for any set $X$?

Brezis' exercise 8.28.2: prove that $T$ is a compact operator

Is there an alternative proof for $\lim a_n^{\frac{1}{q}}=(\lim a_n)^{\frac1q}$?

Easy proof or generalization of a fact about sequences of substructures

Evaluating a finite sum.

Rotations alternative proofs?

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