Numbers from 1 to 10

Math

Here are the constants and numbers from 1 to 10.

\(\phi-0.5=\sqrt{\frac54}\)
The square root of 1.25 is occasionally used in a pentagon. It is approximately equal to 1.1180339887499.

\(\sqrt[4]{2}\)
The fourth root of 2 is also the square root of the square root of 2. It is approximately equal to 1.189207115.

1.2
1.2 is equal to $1 1⁄5$.

\(\sqrt{\frac32}\)
The square root of 1|1.5 is not important but is useful in geometry, while using the Pythagorean theorem. It is approximately equal to 1.224745.

1.25
1.25 is equal to $1 1⁄4$.

1.3
1.3 is equal to $1 3⁄10$.

Plastic number
It is an algebraic number as it is the real solution of the cubic equation \(x^3=x+1\). It is approximately equal to 1.324717957.

1.4
1.4 is equal to $1 2⁄5$.

Square root of 2
The square root of 2 is the first number to be proven irrational. It is approximately equal to 1.414213562.

1.5
1.5 is the half point from 1 to 2.

1.6
1.6 is equal to $1 3⁄5$.

Golden ratio
The golden ratio is an important number which can be represented in two ways: &#966; and &#981;. It is the unique positive solution to the quadratic equation \(x^2=x+1\). It is approximately equal to 1.6180339887499.

1.7
1.7 is equal to $1 7⁄10$.

Square root of 3
Although not as commonly used as the square root of 2, the square root of 3 is as important as the square root of 2. It is approximately equal to 1.732050808.

1.75
1.75 is equal to $1 3⁄4$.

1.8
1.8 is equal to $1 4⁄5$.

Third harmonic number
It is \(\sum_{n=0}^3\frac1n=1\frac56\), which is equal to 1.8.

1.9
1.9 is equal to $1 9⁄10$.

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