Predictably Irrational – The Hidden Forces That Shape Our Decisions By Dan Ariely “If I were to distill one main lesson from the research described in this book, it is that we are pawns in a game whose

everything units can do! And units… ...are closed under products and rational powers. ...support irrational values such as π.Vector space magnitudes https://aurora-opensource.github.io/au/main/discussi everything units can do! And units… ...are closed under products and rational powers. ...support irrational values such as π. std::ratio: N D Vector space magnitudes: ∏ibpi iVector space magnitudes everything units can do! And units… ...are closed under products and rational powers. ...support irrational values such as π. std::ratio: N D Vector space magnitudes: ∏ibpi i AU m M = 149 597 870

arises in squares with sides of unit length. The length of the diagonals of these squares is irrational. This discovery was a serious blow to the Greek mathematicians. The Greeks discovered 2000 years is that some quantities, such as the length of the diagonal of a square with unit sides, are irrational. This discovery was a serious blow to the Greek mathematicians. 21 706.015 Introduction to Scientific

between the bits A common way to find a pattern of such bits is to use the binary expansion of an irrational number. In this case, that number is the reciprocal of the golden ratio: φ = (1 + sqrt(5))

magnitudes – electronvolt ( ) – Dalton ( ) • Some conversions require a conversion factor based on an irrational number like pi – radian <-> degree CppCon 2024: Improving our safety with a quantities and units

│ ├─ UInt32 │ ├─ UInt64 │ └─ UInt128 ├─ Rational └─ AbstractIrrational (Abstract Type) └─ Irrational Abstract number types Core.Number – Type. Number 790CHAPTER 44. NUMBERS 791 Abstract supertype Base.AbstractIrrational – Type. AbstractIrrational <: Real Number type representing an exact irrational value, which is automatically rounded to the correct precision in arithmetic operations with other Rationals are checked for overflow. source Base.Irrational – Type. Irrational{sym} <: AbstractIrrational Number type representing an exact irrational value denoted by the symbol sym, such as π, and γ

│ ├─ UInt32 │ ├─ UInt64 │ └─ UInt128 ├─ Rational └─ AbstractIrrational (Abstract Type) └─ Irrational Abstract number types Core.Number – Type. Number 790CHAPTER 44. NUMBERS 791 Abstract supertype Base.AbstractIrrational – Type. AbstractIrrational <: Real Number type representing an exact irrational value, which is automatically rounded to the correct precision in arithmetic operations with other Rationals are checked for overflow. source Base.Irrational – Type. Irrational{sym} <: AbstractIrrational Number type representing an exact irrational value denoted by the symbol sym, such as π, and γ

Base.AbstractIrrational – Type. AbstractIrrational <: Real Number type representing an exact irrational value, which is automatically rounded to the correct precision in arithmetic operations with other source Base.Irrational – Type. Irrational{sym} <: AbstractIrrational Number type representing an exact irrational value denoted by the symbol sym, such as π, and γ. See also [@irrational], AbstractIrrational A::AbstractMatrix) Matrix exponential, equivalent to exp(log(b)A). Julia 1.1 Support for raising Irrational numbers (like ) to a matrix was added in Julia 1.1. Examples julia> 2^[1 2; 0 3] 2×2 Matrix{Float64}:

Base.AbstractIrrational – Type. AbstractIrrational <: Real Number type representing an exact irrational value, which is automatically rounded to the correct precision in arithmetic operations with other source Base.Irrational – Type. Irrational{sym} <: AbstractIrrational Number type representing an exact irrational value denoted by the symbol sym, such as π, and γ. See also [@irrational], AbstractIrrational A::AbstractMatrix) Matrix exponential, equivalent to exp(log(b)A). Julia 1.1 Support for raising Irrational numbers (like ) to a matrix was added in Julia 1.1. Examples julia> 2^[1 2; 0 3] 2×2 Matrix{Float64}:

Base.AbstractIrrational – Type. AbstractIrrational <: Real Number type representing an exact irrational value, which is automatically rounded to the correct precision in arithmetic operations with other source Base.Irrational – Type. Irrational{sym} <: AbstractIrrational Number type representing an exact irrational value denoted by the symbol sym, such as π, and γ. See also [@irrational], AbstractIrrational A::AbstractMatrix) Matrix exponential, equivalent to exp(log(b)A). Julia 1.1 Support for raising Irrational numbers (like ) to a matrix was added in Julia 1.1. Examples julia> 2^[1 2; 0 3] 2×2 Matrix{Float64}: