My T-shirt designs

I list the writings I have put on my t-shirts.

My T-shirt designs
Seventy-Five
25*15 – 10*30 = 75
26*16 – 11*31 = 75
27*17 – 12*32 = 75
28*18 – 13*33 = 75
29*19 – 14*34 = 75
30*20 – 15*35 = 75
31*21 – 16*36 = 75
32*22 – 17*37 = 75
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The sum of products is a product.
For all numbers, A, B, C,
(A-B) * (A+B) + (B-C) * (B+C) = (A-C) * (A+C)
This algebraic identity implies that
x1 * y1 + x2 * (y1-x1-x2) = ((y1-y2+x1+x2)/2) * ((y1+y2+x1-x2)/2)
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Seventy-Four
3 * 36 – 1 * 34 = 74
4 * 35 – 2 * 33 = 74
5 * 34 – 3 * 32 = 74
6 * 33 – 4 * 31 = 74
7 * 32 – 5 * 30 = 74
8 * 31 – 6 * 29 = 74
9 * 30 – 7 * 28 = 74
10 * 29 – 8 * 27 = 74
11 * 28 – 9 * 26 = 74
12 * 27 – 10 * 25 = 74
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Seventy-Two
2*2*2*3*3 = 72
2*[2*2*3*3] = 72
2*36 = 72
[2*2*2*3]*3 = 72
24 * 3 = 72
[2*2]*[2*3*3] = 72
4 * 18 = 72
[2*3]*[2*2*3] = 72
6 * 12 = 72
[2*2*2]*[3*3] = 72
8 * 9 = 72
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Prime Integers
2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are the first 10 positive prime integers.
Any positive integer can be written as a product of primes in exactly one way, except for the order in which they are written.
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Pythagorean Triple
If x^2 + y^2 = z^2 and a^2 + b^2 = c^2 then
[1] (a*x – b*y)^2 + (a*g + b*x)^2 = (c*z)^2
[2] (a*x + b*y)^2 + (a*g - b*x)^2 = (c*z)^2
[3] (by)^2 + (a*z + c*x)^2 = (c*z + a*x)^2
Proof:
(c^2 *z^2) + a^2 * x^2 – c^2 * x^2 – a^2 * z^2 = c^2 * y^2 – a^2 * y^2 = b^2 * y^2
[4] (by)^2 + (a*z - c*x)^2 = (c*z - a*x)^2
[5] (ay)^2 + (b*z + c*x)^2 = (c*z + b*x)^2
[6] (ay)^2 + (b*z - c*x)^2 = (c*z - b*x)^2
[7] (bx)^2 + (a*z + c*y)^2 = (c*z + a*y)^2
[8] (bx)^2 + (a*z - c*y)^2 = (c*z - a*y)^2
[9] (ax)^2 + (b*z + c*y)^2 = (c*z + b*y)^2
[10] (ax)^2 + (b*z - c*y)^2 = (c*z - b*y)^2
[11] (h^ – n*k^2)^2 + n * (2*h*k)^2 = (h^2 + n*k^2)^2
***
Generalized Pythagorean Triple
If x^2 + y^2 = z^2, then for any integer q,
((2^q^2-1) *x – (2*q)*y + (2*q^2) * z)^2 + ((2*q)*x -y + (2*q)*z))^2
= ((2*q^2)*x-(2*q)*y+(2*q^2+1)*z)^2
A special case is when q = -1.
(x+2*y+2*z)^2 + (2*x+y+2*z)^2 = (2*x+2*y+3*z)^2
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Sums of consecutive odd positive integers
The sum of an odd number of 3 or more consecutive odd positive integers is a composite integer.
5+3+1 = 9
7+5+3 = 15
9+7+5 = 21
9+7+5+3+1 = 25
Every composite odd positive integer is the sum of 3 or more consecutive odd positive integers.
77 = 5+7+9+11+13+15+17
***
Seventy-Three
24*50 - 23*49 = 73
23*51 – 22*50 = 73
22*52 – 21*51 = 73
21*53 – 20*52 = 73
20*54 – 19*53 = 73
19*55 – 18*54 = 73
18*56 – 17*55 = 73
17*57 – 16*56 = 73
16*58 – 15*57 = 73
15*59 – 14*58 - 73
***
(A+B)^2 = A^2 + (2*A+B)*B
(1+1)^2 = 1^2 + (2*1+1)*1 = 1 + 3*1 = 4 = 2*2
(2+1)^2 = 2^2 + (2*2+1)*1 = 4 + 5*1 = 9 = 3^2
(3+1)^2 = 3^2 + (2*3+1)*1 = 9 + 7*1 = 16 = 4^2
(3+2)^2 = 3^2 + (2*3+2)*2 = 9 + 8*2 = 25 = 5^2
***
Difference of Squares
Every odd integer is the difference of two square integers, most of them in 2 or more ways.
Which integers are the difference of two squares in only one way?

(a + b) * (a - b) = (a^2 – b^2)
(3 + 2) * (3 - 2) = 3^2 – 2^2
5 * 1 = 9 – 4

(4 + 1) * (4 - 1) = 4^2 – 1^2
5 * 3 = 16 – 1

(5 + 2) * (5 - 2) = 5^2 – 2^2
7 * 3 = 25 – 4

(6 + 1) * (6 - 1) = 6^2 – 1^2
7 * 5 = 36 – 1

(7 + 2) * (7 - 2) = 7^2 – 2^2
9 * 5 = 49 – 4

***
Sum of four squares
(2 * a + 1)^2 + (2 * b + 1)^2 + (2 * c + 1)^2 + (2 * d + 1)^2
= (a + b + c +d + 2)^2 + (a + b – c - d)^2 + (a – b + c - d)^2 + (a – b – c + d)^2
= (a – b – c – d -1)^2 + (a – b + c + d + 1)^2 + (a + b – c + d + 1)^2 + (a + b + c – d + 1)

4 * (a^2 + b^2 + c^2 + d^2)
= (a + b + c + d)^2 + (a + b – c - d)^2 + (a – b + c - d)^2 + (a – b – c + d)^2
= (a + b + c - d)^2 + (a + b – c + d)^2 + (a – b + c + d)^2 + (a – b – c - d)^2
***
The only person who can stress me is me. I choose not to be stressed.
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Blessed are they who do not insist on their own way, but seek first truth and wisdom, for they will learn from others,
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Blessed are they who are kind and gentle, for they shall reap what they sow.
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Blessed are they who prefer several good answers over the one perfect answer, for they shall be satisfied.
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Blessed are they who respect the needs of others, for they shall have no enemies.
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Blessed are they who seek cooperation in solving problems, for they shall know the joy of working together.
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Blessed are they who are trustworthy, for they shall inspire trust.
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Blessed are they who seek wisdom rather than power, for they shall neither fear nor cause fear.
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Blessed are they who seek good for their neighbors and for themselves, for they shall have peace.
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Avoid judgmentally criticizing yourself because it tends to make you hide yourself from yourself.
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Blessed are they who are free from expectations, for they shall indeed be free.
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Think positively. No matter what goes wrong, you can handle it.
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Blessed are they who accept others unconditionally, for they shall be called angels.
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Twice blessed are they who enjoy life, for they know what is good.
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Wedding vows
We pledge:
To share values and goals:
To clearly express our needs to each other:
To be sensitive to each other’s feelings:
To never let our differences divide us:
To anticipate each other’s needs:
To accept each other wholly in love and honor:
To never judge or condemn each other:
To desire each other’s happiness:
To always to open, honest, and faithful to each other:
To let kindness and gentleness direct our relationship:
To enjoy life together.
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Question: How do you handle it when someone does you wrong?
Answer: Well…From their point of view, they did right. I don’t take it personally.
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The Best Way
The best way to be your own master is to be your own servant.
The best way to know who you are is to be amused at yourself and never judgmentally criticize yourself.
The best thing you can do for yourself is to be altruistic.
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Get Real.
Be Rational,
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Being Altruistic is the best thing you can do for yourself.
… Bob Tzu Duhism Master
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Contrary to the rumors, my relationship with the divine is purely platonic.
… Bob Tzu Duhism Master