In a regular triangle. (isosceles, right, or acute), the interior angles always add up to 180 degrees because in simplest terms, a triangle is basically a line that has been folded into three sections and every line is equivalent to 180 degrees. However... there are technically triangles that have interior angles that do not add up to 180 degrees! A pseudosphere is a triangle that is essentially "drawn" on a sphere resulting in each of the sides being curved. The interior angles of a pseudosphere actually add up to more than 180 degrees.

There are hundreds of terms associated with Geometry. A list of sixteen Geometry terms starting with just the letter P are Pythagorean theorem, Pi, pyramid, polygon, parabola, polytope, points, planes, projective geometry, platonic solids, parallel, power center, pedal triangle, prototile, polyhedron, and pseudosphere.

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +

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152

50

10 x 10=100. Would you rather go like this: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100?

64

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10

1 1 1 1 1 1 1 1 1 1 5 5 5

1 1 1 1 1 1 1 1 1 1 5 10

1 1 1 1 1 5 5 5 5

1 1 1 1 1 5 5 10

1 1 1 1 1 10 10

5 5 5 5 5

5 5 5 10

5 10 10

12 ways

1+1+1+1+1+1+1+1+1+1+1+1+1=13 3 divided by 10 = 30

I assume by "square numbers" you mean perfect squares.

You didn't say how many of each were allowed:

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1²= 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 4² = 23

1² + 1² + 1² + 1² + 1² + 3² + 3² = 23

1² + 1² + 1² + 2² + 2² + 2² + 2² + 2²= 23

1² + 1² + 1² + 2² + 4² = 23

-29

1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1.

Or

1.1 and 1.1 and 1.1 and 42.7

or an infinite number of other possibilities.

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

11111 x 11111 = 123454321

1 1 1 1 1

x 1 1 1 1 1

_______________

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

+ 1 1 1 1 1

_______________

1 2 3 4 5 4 3 2 1

[Legend: Each number represents the denomination (amount) of the coin.]

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+10 = 25

1+1+1+1+1+1+1+1+1+1+5+5+5 = 25

1+1+1+1+1+5+5+10 = 25

1+1+1+1+1+5+5+5+5 = 25

1+1+1+1+1+10+10 = 25

5+5+5+5+5 = 25

5+5+5+10 = 25

5+10+10 = 25

So the answer is 11!!!

I think you're missing 1+1+1+1+1+1+1+1+1+1+5+10 = 25 ?

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is one example.

20

The answer is -1.

(1 + 1 x 1)/(1 - 1 x 1 -1) + 1 =

Follow the order of operations: parentheses/brackets, exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Numerator:

Simplify 1 x 1 to 1.

(1 + 1)/(1 - 1 x 1 -1) + 1

Simplify 1 + 1 to 2.

2/(1 - 1 x 1 - 1) + 1

Denominator:

Simplify 1 x 1 to 1.

2/(1 - 1 - 1) + 1

Simplify 1 - 1 - 1 to -1.

2/(-1) +1

Simplify 2/(-1) to -2.

-2 +1

Simplify.

-1

11

There are infinitely many possible solutions. One of them is

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 12

1+1 is 2 and 1-1 is 0 and 1*1 is 1 and 1/1 is 1

23

One possibility:

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 x 0

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1x0=

They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

1 quarter, 2 dimes, 2 nickels, and 45 pennies

1+2+2+45=50

25+10+10+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100

1 quarter, 2 dimes, 2 nickels, and 45 pennies.

1+2+2+45=50

25+10+10+5+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

The reciprocal of 1 is 1.

Proof:

a. 1*(1/1) = 1 because a*(1/a) = 1

b. 1*1 =1 because 1*a = a

c. 1/1 = 1 compare a. and b.

1+1-1+1-1+1-1+1-1+1-1+1-1+1-1*0+2

1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 19

1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 12 1 11 1 1 1

There are infinitely many possible answers.

One such is 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+16

It is negative infinity.

A series if digits

1

There are infinitely many possible answers:

One possible answer:

-1 and - 1 and - 1 and - 1 and - 1 and - 1 and - 1 and - 1

that is (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1)

1+1+1+1+1+1+1+1+1-1+1+1+1+1x0=

1 x ( 1/1) = 1 ; -1 (1/-1) = 1

(1+1)×(1+1) +1+1

it is 8

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 11 - 9,999,999 = - 9,999,978

you take 1 of the 1s and put it in the tenths place. Then you add the 1+1+1+1+1 and put the answer(5) in the ones place! that is how you get 15 out of 1 1 1 1 1 1.

1+1+1+1+254

1+1+1+2+253

1+1+1+3+252

1+1+1+4+251

and

1*1*1*1*258

Inelegant solution.

Maximum effort.

100-1-1-1-1-1-1-1=

99-1-1-1-1-1-1=

98-1-1-1-1-1=

97-1-1-1-1=

96-1-1-1=

95-1-1

94-1=

93

..... ..... ..... ..... ..... ..... ..... .....

Elegant solution.

Minimum effort.

100-1-1-1-1-1-1-1=

100-7=

93