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https://issues.apache.org/jira/browse/ARROW-11151?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17260060#comment-17260060
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Kouhei Sutou commented on ARROW-11151:
--------------------------------------

The Apache Arrow formula in Homebrew should ensure using the Python installed 
by Homebrew.

The following patch (CMake parameter name was changed because we switched to 
use https://cmake.org/cmake/help/latest/module/FindPython3.html from 
https://cmake.org/cmake/help/latest/module/FindPythonLibs.html) will solve this 
case even when you have another installed Pythons:

{noformat}
diff --git a/Formula/apache-arrow.rb b/Formula/apache-arrow.rb
index 57d43652eb..d2f2a3a9cd 100644
--- a/Formula/apache-arrow.rb
+++ b/Formula/apache-arrow.rb
@@ -57,7 +57,7 @@ class ApacheArrow < Formula
       -DARROW_WITH_SNAPPY=ON
       -DARROW_WITH_BROTLI=ON
       -DARROW_INSTALL_NAME_RPATH=OFF
-      -DPYTHON_EXECUTABLE=#{Formula["python@3.9"].bin/"python3"}
+      -DPytnon3_EXECUTABLE=#{Formula["python@3.9"].bin/"python3"}
     ]
 
     mkdir "build" do
{noformat}

Could you send a pull request to https://github.com/homebrew/homebrew-core ?
See also: https://docs.brew.sh/How-To-Open-a-Homebrew-Pull-Request

> [Python][Packaging] Fix Homebrew Install Python 3 NumPy not found failure
> -------------------------------------------------------------------------
>
>                 Key: ARROW-11151
>                 URL: https://issues.apache.org/jira/browse/ARROW-11151
>             Project: Apache Arrow
>          Issue Type: Bug
>          Components: Packaging, Python
>            Reporter: Ian Cook
>            Priority: Major
>
> {{brew install apache-arrow --HEAD}} fails when there is no existing 
> installation of NumPy.
> {code:java}
> CMake Error at 
> /usr/local/Cellar/cmake/3.19.2/share/cmake/Modules/FindPackageHandleStandardArgs.cmake:218
>  (message):
>   Could NOT find Python3 (missing: Python3_NumPy_INCLUDE_DIRS NumPy) (found
>   version "3.9.1")
> Call Stack (most recent call first):
>   
> /usr/local/Cellar/cmake/3.19.2/share/cmake/Modules/FindPackageHandleStandardArgs.cmake:582
>  (_FPHSA_FAILURE_MESSAGE)
>   
> /usr/local/Cellar/cmake/3.19.2/share/cmake/Modules/FindPython/Support.cmake:3148
>  (find_package_handle_standard_args)
>   /usr/local/Cellar/cmake/3.19.2/share/cmake/Modules/FindPython3.cmake:398 
> (include)
>   cmake_modules/FindPython3Alt.cmake:55 (find_package)
>   src/arrow/python/CMakeLists.txt:22 (find_package)
> {code}
> Workaround is to first install NumPy with {{pip3 install numpy}}.
> Tested in macOS Big Sur 11.1 on an Intel Mac with
>  {{python}} --> Python 2.7.16
>  {{python3}} --> Python 3.9.1



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