Bash Triangle
triangle() {
    local -n _a="$1"
    local -a _sorted=($(printf '%s\n' "${_a[@]}" | sort -n))
    local _c=${#_sorted[@]}
    if (( _c < 3 )); then
        echo 0
        return
    fi
    local _i
    for ((_i = 0; _i < _c - 2; _i++)); do
        if (( _sorted[_i] > 0 && _sorted[_i] > _sorted[_i+2] - _sorted[_i+1] )); then
            echo 1
            return
        fi
    done
    echo 0
}

This sorts the values and checks nearby triples, because a valid triangle only needs one local match after sorting.