There's a black hole in the number line, & other misc. math nonsense

Jerry Tuttle, FCAS, MA, MA, MS

Southern New Hampshire Univ.

2024

Outline

1. Next number in the sequence
2. Harder order of operations
3. Math nonsense in pictures
4. There’s a black hole in the number line

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2024

Find the next Y number in this sequence

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Newton Forward Difference Formula

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Forward Diff Formula

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f(x) = 46 + (x – 1)*20  + (x – 1)(x - 2)*

(-5)/2! + (x – 1)(x - 2)(x – 3)*(2)/3! 

+ (x – 1)(x - 2)(x – 3)(x – 4)*(-3)/4!

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f(x) = (-1/8)x⁴ + (19/12) x³ + (-71/8) x² + (449/12)x + 16.

f(1) = 46, f(2) = 66, f(3) = 81, f(4) = 93

f(5) = f(6) = 101.

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Did you guess the 6^th number is the same as the 5^th number?

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Or, maybe f(6) = -14?

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f(x) = -.9583 x⁵ + 14.25 x⁴ -79.875 x³ + 206.75 x² - 225.1667 x + 131

f(6) = -14

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PEMDAS: Please excuse my dear Aunt Sally

It’s time to stop making excuses for Aunt Sally. Some harder order of ops:

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OR �OR vs AND

I will hire you if years college >= 4 or years experience >=3 and gpa >=3.5; otherwise, I will not hire you.

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1. (College or Experience) and GPA: (True) and False = False; don’t hire.

2. College or (Experience and GPA): True or (False) = True; hire.

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Successive Exponents

Is

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Left associative

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or

Right associative

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Left: Excel.

Right: Google, Python, R, WolframAlpha.

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Misc. order of ops

1. Unary operator (only one operand): -3² = -9, except in Excel.
2. Not A or B ≡ (Not A) or B
3. Comparison operator <, > precedes exponetiation: 2 ^ 3 < 3 ^2
4. Concatenation of strings is not commutative: a + b ≠ b + a when a = “bird” and b = “song”.

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Nonsense math pictures

Use the Pythagorean Theorem to calculate C:

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A = √ - 1

C = ?

B = 1

"I think, therefore I am."

P: I think ⇒ I am.

Q: I think not ⇒ I am not.

Q is called the inverse of P.

Are P and Q logically equivalent ?

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Counting left & right

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1, 2, 3, 4, 5 6, 7, 8, 9, 10

10, 9, 8, 7, 6 plus 5 equals 11 ?

"Designed designed designed

Designed by gstudioimagen / Freepik

Nonsense math picture

She’s a singer, songwriter, businesswoman, philanthropist; and more!

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There’s a black hole in the number line

Once you fall into it, you can never get out.

Our government knows about this, but keeps it secret.

The hole is an integer somewhere between 3.99 and 4.01. Shhhhhhhh.

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Any word in English has the same black hole, at four. mathematics

Mathematics has 11 letters

Eleven has six letters

Six has three letters

Three has five letters

Five has four letters

Four has four letters

Four has four letters

Four has four letters …

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2024

In German the black hole is vier: Mathematik

Mathematik has zehn (10) letters

Zehn has vier (4) letters

Vier has vier (4) letters

Vier has vier (4) letters

Vier has (4) letters …

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2024

In Spanish the black hole is cinco, but sometimes the hole oscillates between cuatro and seis: matematicas

matematicas has once (11) letters

Once has cuatro (4) letters

Cuatro has seis (6) letters

Seis has cuatro (4) letters

Cuatro has seis (6) letters …

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In Hebrew the black �holes are� שלש (3) and  ארבע (4).�mathematics is �מָתֵימָטִיקָה

מָתֵימָטִיקָה has שמונה (8) letters

שמונה has חמש (5) letters

חמש has שלש (3) letters

שלש has שלש (3) letters …

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Some languages have no black hole

French is one example. ��There’s a joke here somewhere, but I don’t know what it is.

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If you try a few examples, you’ll see why the hole in English is at four.

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Thanks for listening!

2024